what is a one-way repeated measures anova?
DESCRIPTION
What is a one-way repeated measures ANOVA?TRANSCRIPT
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Repeated Measures (ANOVA)
Conceptual Explanation
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How did you get here?
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How did you get here?So, you have decided to use a Repeated Measures ANOVA.
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How did you get here?So, you have decided to use a Repeated Measures ANOVA.Let’s consider the decisions you made to get here.
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First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
![Page 6: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/6.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
![Page 7: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/7.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Sample of 30
![Page 8: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/8.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Sample of 30
Generalizes to
![Page 9: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/9.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Large Population of 30,000
Sample of 30
Generalizes to
![Page 10: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/10.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Large Population of 30,000
Sample of 30
Generalizes to
![Page 11: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/11.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
![Page 12: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/12.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Double check your problem to see if that is the case
![Page 13: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/13.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Inferential Descriptive
Double check your problem to see if that is the case
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit. Inferential Descriptive
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Relationship
![Page 17: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/17.jpg)
You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
DifferenceDifference Relationship
![Page 18: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/18.jpg)
You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of FitDifference Relationship
![Page 19: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/19.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of FitDifference Relationship
![Page 20: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/20.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Ratio/Interval
Difference Relationship
![Page 21: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/21.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
OrdinalRatio/Interval
Difference Relationship
![Page 22: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/22.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
NominalOrdinalRatio/Interval
Difference Relationship
![Page 23: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/23.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
![Page 24: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/24.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
![Page 25: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/25.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
![Page 26: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/26.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
![Page 27: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/27.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed
NominalOrdinalRatio/Interval
Difference Relationship
![Page 28: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/28.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic
NominalOrdinalRatio/Interval
Difference Relationship
![Page 29: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/29.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
NominalOrdinalRatio/Interval
Difference Relationship
![Page 30: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/30.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
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Only one Dependent Variable (DV) rather than two or more exist.
DV #1
Chemistry Test Scores
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Only one Dependent Variable (DV) rather than two or more exist.
DV #1 DV #2
Chemistry Test Scores
Class Attendance
![Page 33: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/33.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
DV #1 DV #2 DV #3
Chemistry Test Scores
Class Attendance
Homework Completed
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Only one Dependent Variable (DV) rather than two or more exist.
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
Double check your problem to see if that is the case
NominalOrdinalRatio/Interval
Difference Relationship
![Page 35: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/35.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV
Double check your problem to see if that is the case
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
![Page 36: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/36.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
Inferential Descriptive
Difference Relationship Difference Goodness of Fit
Ratio/Interval Ordinal Nominal
Skewed Kurtotic Normal
1 DV 2+ DV
Double check your problem to see if that is the case
![Page 37: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/37.jpg)
Only one Independent Variable (DV) rather than two or more exist.
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Only one Independent Variable (DV) rather than two or more exist.
IV #1
Use of Innovative eBook
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Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2
Use of Innovative eBook
Doing Homework to Classical Music
![Page 40: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/40.jpg)
Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2 IV #3
Use of Innovative eBook
Doing Homework to Classical Music Gender
![Page 41: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/41.jpg)
Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2 IV #3
Use of Innovative eBook
Doing Homework to Classical Music Gender
![Page 42: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/42.jpg)
Only one Independent Variable (DV) rather than two or more exist.
![Page 43: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/43.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
![Page 44: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/44.jpg)
Only one Independent Variable (DV) rather than two or more exist. Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
![Page 45: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/45.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Nominal
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV 2+ IV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship Difference
![Page 46: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/46.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV 2+ IV
Double check your problem to see if that is the case
Inferential
NominalOrdinalRatio/Interval
Difference Relationship Difference
![Page 47: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/47.jpg)
There are three levels of the Independent Variable (IV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
![Page 48: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/48.jpg)
There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1
Before using the innovative ebook
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There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1 Level 2
Before using the innovative ebook
Using the innovative ebook
for 2 months
![Page 50: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/50.jpg)
There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1 Level 2 Level 3
Before using the innovative ebook
Using the innovative ebook
for 2 months
Using the innovative ebook
for 4 months
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Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DVs
2+ IVs
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
2 levels 3+ levels
1 IV
Difference
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The samples are repeated rather than independent. Notice that the same class (Chem 100 section 003) is repeatedly tested.
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The samples are repeated rather than independent. Notice that the same class (Chem 100 section 003) is repeatedly tested.
Chem 100 Section 003
January
Chem 100 Section 003
March
Chem 100 Section 003
May
Before using the innovative
ebook
Using the innovative ebook
for 2 months
Using the innovative ebook
for 4 months
![Page 54: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/54.jpg)
Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DVs
2+ IVs
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
2 levels 3+ levels
1 IV
Difference
RepeatedIndependent
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If this was the appropriate path for your problem then you have correctly selected Repeated-measures ANOVA to solve the problem you have been presented.
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Repeated Measures ANOVA –
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Repeated Measures ANOVA –Another use of analysis of variance is to test whether a single group of people change over time.
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Repeated Measures ANOVA –Another use of analysis of variance is to test whether a single group of people change over time.
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In this case, the distributions that are compared to each other are not from different groups
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In this case, the distributions that are compared to each other are not from different groups
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
But from different times.
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
But from different times.
versus
Group 1 Group 2
Group 1 Group 1: Two Months Later
versus
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
January FebruaryApril
Exam 1Exam 2
Exam 3
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
![Page 67: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/67.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
![Page 68: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/68.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
![Page 69: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/69.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
![Page 70: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/70.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
There is a difference but
we don’t know where
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Post hoc tests will reveal exactly where the differences occurred.
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Post hoc tests will reveal exactly where the differences occurred.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score 35
Average Score 38
Average Score 40
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Post hoc tests will reveal exactly where the differences occurred.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score 35
Average Score 38
Average Score 40
There is a statistically significant
difference only between Exam 1
and Exam 3
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In contrast, with the One-way analysis of Variance (ANOVA) we were attempting to determine if there was a statistical difference between 2 or more (generally 3 or more) groups.
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In contrast, with the One-way analysis of Variance (ANOVA) we were attempting to determine if there was a statistical difference between 2 or more (generally 3 or more) groups.In our One-way ANOVA example in another presentation we attempted to determine if there was any statistically significant difference in the amount of Pizza Slices consumed by three different player types (football, basketball, and soccer).
![Page 76: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/76.jpg)
The data would be set up thus:
![Page 77: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/77.jpg)
The data would be set up thus:Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 78: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/78.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 79: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/79.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 80: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/80.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)A Repeated Measures ANOVA is different than a One-Way ANOVA in one simply way: Only one group of person or observations is being measured, but they are measured more than one time.
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 81: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/81.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)A Repeated Measures ANOVA is different than a One-Way ANOVA in one simply way: Only one group of persons or observations is being measured, but they are measured more than one time.
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 82: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/82.jpg)
Notice the different times football player pizza consumption is being measured.
Football Players
Pizza Slices
Consumed
Pizza Slices Consumed
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 83: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/83.jpg)
Notice the different times football player pizza consumption is being measured.
Football Players
Pizza Slices
ConsumedBefore the
Season
Pizza Slices Consumed
During the Season
Pizza Slices Consumed
After the Season
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 84: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/84.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
![Page 85: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/85.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 86: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/86.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
The relationship between the scores is that we are comparing the same person across multiple observations.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 87: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/87.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common:
![Page 88: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/88.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common:
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 89: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/89.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common: THESE SCORES ALL BELONG TO BEN.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 90: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/90.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common: THESE SCORES ALL BELONG TO BEN.
They are subject to all the factors that are special to Ben when consuming pizza, including how much he likes or dislikes, the toppings that are available, the eating atmosphere, etc.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 91: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/91.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.
![Page 92: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/92.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 93: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/93.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 94: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/94.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 95: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/95.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred.
![Page 96: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/96.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred. After running a repeated-measures ANOVA, this is the output that we will get:
![Page 97: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/97.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred. After running a repeated-measures ANOVA, this is the output that we will get:
Tests of Within-Subjects Effects
Measure: Pizza slices
Source
Type III Sum of
Squares dfMean
Square F Sig.
Between Subjects 21.333 4
Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 98: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/98.jpg)
This output will help us determine if we reject the null hypothesis:
![Page 99: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/99.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.
![Page 100: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/100.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.Or accept the alternative hypothesis:
![Page 101: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/101.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.Or accept the alternative hypothesis:There is a significant difference in the amount of
pizza consumed by football players before, during, and/or after the season.
![Page 102: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/102.jpg)
To do so, let’s focus on the value .008
![Page 103: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/103.jpg)
To do so, let’s focus on the value .008Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 104: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/104.jpg)
To do so, let’s focus on the value .008Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 105: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/105.jpg)
To do so, let’s focus on the value .008
This means that if we were to reject the null hypothesis, the probability that we would be wrong is 8 times out of 1000. As you remember, if that were to happen, it would be called a Type 1 error.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 106: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/106.jpg)
To do so, let’s focus on the value .008
This means that if we were to reject the null hypothesis, the probability that we would be wrong is 8 times out of 1000. As you remember, if that were to happen, it would be called a Type 1 error.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 107: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/107.jpg)
But it is so unlikely, that we would be willing to take that risk and hence reject the null hypothesis.
![Page 108: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/108.jpg)
But it is so unlikely, that we would be willing to take that risk and hence we reject the null hypothesis.
There IS NO statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season.
![Page 109: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/109.jpg)
But it is so unlikely, that we would be willing to take that risk and hence we reject the null hypothesis.
There IS NO statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season. REJE
CT
![Page 110: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/110.jpg)
And accept the alternative hypothesis:
![Page 111: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/111.jpg)
And accept the alternative hypothesis:
There IS A statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season.
![Page 112: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/112.jpg)
And accept the alternative hypothesis:
There IS A statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season. ACCEPT
![Page 113: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/113.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
![Page 114: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/114.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 115: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/115.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 116: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/116.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Later, we can run what is called a “Post-hoc” test to determine where the difference lies.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 117: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/117.jpg)
From this point on – we will delve into the actual calculations and formulas that produce a Repeated-measures ANOVA. If such detail is of interest or a necessity to know, please continue.
![Page 118: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/118.jpg)
How was a significance value of .008 calculated?
![Page 119: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/119.jpg)
How was a significance value of .008 calculated?Let’s begin with the calculation of the various sources of Sums of Squares
![Page 120: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/120.jpg)
How was a significance value of .008 calculated?Let’s begin with the calculation of the various sources of Sums of Squares
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 121: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/121.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.
![Page 122: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/122.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?
![Page 123: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/123.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?• Is it differences between times (before,
during, and after)?
![Page 124: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/124.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?• Is it differences between times (before,
during, and after)?Remember, the full name for sum of squares is the sum of squared deviations about the mean. This will help us determine the amount of variation from each of the possible sources.
![Page 125: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/125.jpg)
Let’s begin by calculating the total sums of squares.
![Page 126: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/126.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 127: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/127.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 128: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/128.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means one pizza eating observation for person “I” (e.g., Ben) on
time “j” (e.g., before)
![Page 129: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/129.jpg)
For example:
![Page 130: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/130.jpg)
For example: Pizza Slices Consumed
Football Players Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 131: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/131.jpg)
For example: Pizza Slices Consumed
Football Players Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 132: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/132.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 133: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/133.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 134: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/134.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 135: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/135.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 136: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/136.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 137: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/137.jpg)
For example:
ETC
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 138: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/138.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 139: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/139.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
![Page 140: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/140.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observationsThis means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 141: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/141.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 142: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/142.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Average of All Observations
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 143: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/143.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
![Page 144: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/144.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
This means the average of
all of the observations
�́�𝑿
![Page 145: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/145.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
This means the average of
all of the observations
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 146: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/146.jpg)
Let’s calculate total sums of squares with this data set:
![Page 147: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/147.jpg)
Let’s calculate total sums of squares with this data set:
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 148: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/148.jpg)
To do so we will rearrange the data like so:
![Page 149: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/149.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
![Page 150: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/150.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
![Page 151: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/151.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 152: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/152.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 153: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/153.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 154: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/154.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
Each observation
![Page 155: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/155.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 156: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/156.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 157: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/157.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 158: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/158.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
Average of All Observations =
6.3
![Page 159: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/159.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
![Page 160: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/160.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 161: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/161.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
To do so we will rearrange the data like so:We
will subtract each of these values from the
grand mean, square the result and sum
them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
![Page 162: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/162.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values
from the grand mean,
square the result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3 =Bob Before 7 - 6.3 =Bud Before 8 - 6.3 =
Bubba Before 9 - 6.3 =Burt Before 10 - 6.3 =Ben During 4 - 6.3 =Bob During 5 - 6.3 =Bud During 7 - 6.3 =
Bubba During 8 - 6.3 =Burt During 7 - 6.3 =Ben After 4 - 6.3 =Bob After 5 - 6.3 =Bud After 6 - 6.3 =
Bubba After 4 - 6.3 =Burt After 6 - 6.3 =
![Page 163: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/163.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values
from the grand mean,
square the result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3 =Bob Before 7 - 6.3 =Bud Before 8 - 6.3 =
Bubba Before 9 - 6.3 =Burt Before 10 - 6.3 =Ben During 4 - 6.3 =Bob During 5 - 6.3 =Bud During 7 - 6.3 =
Bubba During 8 - 6.3 =Burt During 7 - 6.3 =Ben After 4 - 6.3 =Bob After 5 - 6.3 =Bud After 6 - 6.3 =
Bubba After 4 - 6.3 =Burt After 6 - 6.3 =
Football Players
Season Slices of Pizza
Grand Mean
Deviation
Ben Before 5 - 6.3 = -1.3Bob Before 7 - 6.3 = 0.7Bud Before 8 - 6.3 = 1.7
Bubba Before 9 - 6.3 = 2.7Burt Before 10 - 6.3 = 3.7Ben During 4 - 6.3 = -2.3Bob During 5 - 6.3 = -1.3Bud During 7 - 6.3 = 0.7
Bubba During 8 - 6.3 = 1.7Burt During 7 - 6.3 = 0.7Ben After 4 - 6.3 = -2.3Bob After 5 - 6.3 = -1.3Bud After 6 - 6.3 = -0.3
Bubba After 4 - 6.3 = -2.3Burt After 6 - 6.3 = -0.3
![Page 164: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/164.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values from the grand mean, square the result and sum them all up.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
![Page 165: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/165.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
We will subtract each of these values from the grand mean, square the result and sum them all up.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 166: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/166.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
Then –
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 167: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/167.jpg)
To do so we will rearrange the data like so:
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 168: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/168.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 169: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/169.jpg)
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 170: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/170.jpg)
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 171: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/171.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:
![Page 172: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/172.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)
![Page 173: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/173.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)• Between Groups (this would be between
BEFORE, DURING, AFTER)
![Page 174: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/174.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)• Between Groups (this would be between
BEFORE, DURING, AFTER)• Error (the variance that we cannot explain
with our design)
![Page 175: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/175.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
![Page 176: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/176.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 177: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/177.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
Let’s calculate the sums of squares between subjects.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 178: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/178.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
![Page 179: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/179.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 180: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/180.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 181: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/181.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 2.669 .078
Error 29.600 8 3.700
Total 49.333 14
![Page 182: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/182.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 2.669 .078
Error 29.600 8 3.700
Total 49.333 14
![Page 183: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/183.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).
![Page 184: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/184.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).But the difference in within groups variability is not a function of error, it is a function of Ben, Bob, Bud, Bubba, and Burt’s being different in terms of the amount of slices they eat regardless of when they eat!
![Page 185: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/185.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).But the difference in within groups variability is not a function of error, it is a function of Ben, Bob, Bud, Bubba, and Burt’s being different in terms of the amount of slices they eat regardless of when they eat!
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3Bob 7 5 5 5.7Bud 8 7 6 7.0
Bubba 9 8 4 7.0Burt 10 7 6 7.7
![Page 186: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/186.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
![Page 187: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/187.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
![Page 188: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/188.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
There is no variability between subjects (they are all 5.0).
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
![Page 189: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/189.jpg)
Look at the variability between groups:
![Page 190: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/190.jpg)
Look at the variability between groups: Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
1.8 5.0 8.2
![Page 191: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/191.jpg)
Look at the variability between groups:
They are very different from one another.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
1.8 5.0 8.2
![Page 192: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/192.jpg)
Here is what the ANOVA table would look like:
![Page 193: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/193.jpg)
Here is what the ANOVA table would look like:Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 194: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/194.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 195: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/195.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!But there is a lot of sum of squares values for the between groups.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 196: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/196.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!But there is a lot of sum of squares values for the between groups.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 197: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/197.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:
![Page 198: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/198.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:Here it is:
![Page 199: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/199.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:Here it is:
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0
Bob 5 5 5 5.0
Bud 7 7 7 7.0
Bubba 8 8 8 8.0
Burt 12 12 13 12.3
Between Subjects
![Page 200: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/200.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.
![Page 201: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/201.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.When you see between SUBJECTS averages that far away, you know that the sums of squares for between groups will be very large.
![Page 202: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/202.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.When you see between SUBJECTS averages that far away, you know that the sums of squares for between groups will be very large.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 203: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/203.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
![Page 204: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/204.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
![Page 205: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/205.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
Between Groups
![Page 206: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/206.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
Between Groups
![Page 207: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/207.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
![Page 208: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/208.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 209: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/209.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
Now that we have conceptually considered the sources of variability as described by the sum of squares, let’s begin calculating between subjects, between groups, and the error sources.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 210: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/210.jpg)
We will begin with calculating Between Subjects sum of squares.
![Page 211: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/211.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
![Page 212: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/212.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 213: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/213.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Here is the formula for calculating SS between subjects.
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 214: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/214.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Here is the formula for calculating SS between subjects.
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑋𝑏𝑠− �́� )2
![Page 215: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/215.jpg)
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2
![Page 216: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/216.jpg)
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2 Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3
Bob 7 5 5 5.7
Bud 8 7 6 7.0
Bubba 9 8 4 7.0
Burt 10 7 6 7.7
![Page 217: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/217.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3
Bob 7 5 5 5.7
Bud 8 7 6 7.0
Bubba 9 8 4 7.0
Burt 10 7 6 7.7
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2This means the average of between
subjects
![Page 218: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/218.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus
Ben 5 4 4 4.3 -
Bob 7 5 5 5.7 -
Bud 8 7 6 7.0 -
Bubba 9 8 4 7.0 -
Burt 10 7 6 7.7 -
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2
![Page 219: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/219.jpg)
This means the average of all of the observations
![Page 220: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/220.jpg)
Here is how we calculate the grand mean again:
![Page 221: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/221.jpg)
Here is how we calculate the grand mean again: Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Average of All Observations =
6.3
![Page 222: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/222.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.
![Page 223: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/223.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus Grand Mean
Ben 5 4 4 4.3 - 6.3
Bob 7 5 5 5.7 - 6.3
Bud 8 7 6 7.0 - 6.3
Bubba 9 8 4 7.0 - 6.3
Burt 10 7 6 7.7 - 6.3
This means the average of all of the observations
![Page 224: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/224.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean.
![Page 225: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/225.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus Grand Mean
Deviation
Ben 5 4 4 4.3 - 6.3 -2.0
Bob 7 5 5 5.7 - 6.3 -0.6
Bud 8 7 6 7.0 - 6.3 0.7
Bubba 9 8 4 7.0 - 6.3 0.7
Burt 10 7 6 7.7 - 6.3 1.4
![Page 226: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/226.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.
![Page 227: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/227.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.
![Page 228: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/228.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
![Page 229: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/229.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
![Page 230: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/230.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
![Page 231: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/231.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Sum up
![Page 232: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/232.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.Finally, we multiply the sum all of these squared deviations by the number of groups:
![Page 233: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/233.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 234: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/234.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
Number of conditions
![Page 235: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/235.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 236: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/236.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 237: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/237.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 238: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/238.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 239: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/239.jpg)
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 240: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/240.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 241: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/241.jpg)
Now it is time to compute the between groups (seasons) sum of squares.
![Page 242: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/242.jpg)
Now it is time to compute the between groups’ (seasons) sum of squares.
Here is the equation we will use to compute it:
![Page 243: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/243.jpg)
Now it is time to compute the between groups’ (seasons) sum of squares.
Here is the equation we will use to compute it:
![Page 244: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/244.jpg)
Let’s break this down with our data set:
![Page 245: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/245.jpg)
Let’s break this down with our data set:
![Page 246: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/246.jpg)
Let’s break this down with our data set:
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 247: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/247.jpg)
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 248: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/248.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
We begin by computing the mean of each condition (k)
![Page 249: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/249.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
![Page 250: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/250.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
![Page 251: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/251.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
![Page 252: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/252.jpg)
Then subtract each condition mean from the grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
![Page 253: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/253.jpg)
Then subtract each condition mean from the grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
![Page 254: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/254.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
Then subtract each condition mean from the grand mean.
![Page 255: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/255.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Then subtract each condition mean from the grand mean.
![Page 256: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/256.jpg)
Square the deviation.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
![Page 257: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/257.jpg)
Sum the Squared Deviations:
![Page 258: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/258.jpg)
Sum the Squared Deviations:
![Page 259: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/259.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
Sum
Sum the Squared Deviations:
![Page 260: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/260.jpg)
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
Sum
Sum the Squared Deviations:
3.95
Sum of Squared Deviations
![Page 261: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/261.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
![Page 262: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/262.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
![Page 263: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/263.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
![Page 264: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/264.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
![Page 265: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/265.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
![Page 266: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/266.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 267: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/267.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
![Page 268: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/268.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 269: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/269.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 270: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/270.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 271: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/271.jpg)
So far we have calculated Total Sum of Squares along with Sum of Squares for Between Subjects, and Between Groups.
![Page 272: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/272.jpg)
So far we have calculated Total Sum of Squares along with Sum of Squares along with Sum of Squares for Between Subjects, Between Groups.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 273: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/273.jpg)
Now we will calculate the sum of squares associated with Error.
![Page 274: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/274.jpg)
Now we will calculate the sum of squares associated with Error.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 275: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/275.jpg)
To do this we simply add the between subjects and between groups sums of squares.
![Page 276: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/276.jpg)
To do this we simply add the between subjects and between groups sums of squares.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 277: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/277.jpg)
To do this we simply add the between subjects and between groups sums of squares.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
21.333
Between Subjects Sum of Squares
19.733
Between Groups Sum of Squares
41.600
Between Subjects & Groups Sum of
Squares Combined
![Page 278: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/278.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
![Page 279: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/279.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
49.333
Total Sum of Squares
41.600 Between Subjects &
Groups Sum of Squares Combined
8.267
Sum of Squares Attributed to Error
or Unexplained
![Page 280: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/280.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
49.333
Total Sum of Squares
41.600 Between Subjects &
Groups Sum of Squares Combined
8.267
Sum of Squares Attributed to Error
or Unexplained
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 281: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/281.jpg)
Now we have all of the information necessary to determine if there is a statistically significant difference between pizza slices consumed by football players between three different eating occasions (before, during or after the season).
![Page 282: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/282.jpg)
Now we have all of the information necessary to determine if there is a statistically significant difference between pizza slices consumed by football players between three different eating occasions (before, during or after the season).
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 283: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/283.jpg)
To calculate the significance level
![Page 284: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/284.jpg)
To calculate the significance levelSource
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 285: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/285.jpg)
We must calculate the F ratio
![Page 286: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/286.jpg)
We must calculate the F ratioSource
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 287: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/287.jpg)
Which is calculated by dividing the Between Groups Mean Square value (9.867) by the Error Mean Square value (1.033).
![Page 288: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/288.jpg)
Which is calculated by dividing the Between Groups Mean Square value (9.867) by the Error Mean Square value (1.033).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 289: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/289.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
![Page 290: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/290.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 291: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/291.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 292: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/292.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14 =
=
![Page 293: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/293.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
Now we need to figure out how we calculate degrees of freedom for each source of sums of squares.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14 =
=
![Page 294: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/294.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
![Page 295: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/295.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
![Page 296: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/296.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 297: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/297.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 298: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/298.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 299: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/299.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0
Bob 5 5 5 5.0
Bud 7 7 7 7.0
Bubba 8 8 8 8.0
Burt 12 12 13 12.3
Between Subjects
1
2
3
4
5
![Page 300: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/300.jpg)
Now – onto Between Groups Degrees of Freedom (df)
![Page 301: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/301.jpg)
Now – onto Between Groups Degrees of Freedom (df)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 302: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/302.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 303: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/303.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 304: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/304.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
1 2 3
![Page 305: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/305.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
1 2 3
![Page 306: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/306.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
![Page 307: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/307.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
![Page 308: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/308.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 309: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/309.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 310: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/310.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
![Page 311: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/311.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
![Page 312: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/312.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 313: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/313.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 314: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/314.jpg)
We will compute the Mean Square values for just the Between Groups and Error. We are not interested in what is happening with Between Subjects. We calculated the Between Subjects sum of squares only take out any differences that are a function of differences that would exist regardless of what group we were looking at.
![Page 315: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/315.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
![Page 316: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/316.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 317: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/317.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
![Page 318: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/318.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
![Page 319: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/319.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
Within Groups is another way of
saying Error
![Page 320: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/320.jpg)
And that would have created a larger error mean square value:
![Page 321: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/321.jpg)
And that would have created a larger error mean square value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 322: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/322.jpg)
And that would have created a larger error mean square value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 323: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/323.jpg)
Which in turn would have created a smaller F value:
![Page 324: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/324.jpg)
Which in turn would have created a smaller F value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 325: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/325.jpg)
Which in turn would have created a smaller F value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
=
=
![Page 326: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/326.jpg)
Which in turn would have created a larger significance value:
![Page 327: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/327.jpg)
Which in turn would have created a larger significance value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 328: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/328.jpg)
Which in turn would have created a larger significance value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
=
=
![Page 329: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/329.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.
![Page 330: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/330.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
![Page 331: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/331.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 332: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/332.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 333: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/333.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
And a more accurate F value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 334: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/334.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
And a more accurate F value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 335: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/335.jpg)
…as well as a more accurate Significance value…
![Page 336: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/336.jpg)
…as well as a more accurate Significance value…Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 337: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/337.jpg)
…as well as a more accurate Significance value…
Therefore, we will only focus on mean square values for Between Groups and Error:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 338: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/338.jpg)
…as well as a more accurate Significance value…
Therefore, we will only focus on mean square values for Between Groups and Error:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 339: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/339.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
![Page 340: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/340.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 341: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/341.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
Which gives us an F value of 9.548
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 342: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/342.jpg)
Because we are using statistical software we will also get a significance value of .008. This means that is we were to theoretically run this experiment 1000 times we would be wrong to reject the null hypothesis 8 times this incurring a type 1 error.
![Page 343: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/343.jpg)
Because we are using statistical software we will also get a significance value of .008. This means that is we were to theoretically run this experiment 1000 times we would be wrong to reject the null hypothesis 8 times this incurring a type 1 error.If we are willing to live with those odds of failure (8 out of 1000) then we would reject the null hypothesis.
![Page 344: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/344.jpg)
If we had set our alpha cut off at .05 that would mean we would be willing to take the risk of being wrong 50 out of 1000 or 5 out of 100 times.
![Page 345: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/345.jpg)
If we had set our alpha cut off at .05 that would mean we would be willing to take the risk of being wrong 50 out of 1000 or 5 out of 100 times.If we do not get a significance value (.008) then we could go to the F table to determine if our F value of 9.548 exceeds the F critical value in the F table.
![Page 346: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/346.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
![Page 347: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/347.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 348: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/348.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Error df
![Page 349: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/349.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
![Page 350: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/350.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 351: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/351.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
![Page 352: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/352.jpg)
Now let’s put them together:
![Page 353: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/353.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 354: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/354.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 355: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/355.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 356: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/356.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 357: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/357.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Now let’s put them together:
![Page 358: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/358.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 359: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/359.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 360: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/360.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.Once again, we only show you the table as another way to determine if you have statistical significance.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 361: What is a one-way repeated measures ANOVA?](https://reader037.vdocument.in/reader037/viewer/2022102711/55847909d8b42aca538b5128/html5/thumbnails/361.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.Once again, we only show you the table as another way to determine if you have statistical significance.That’s it. You have now seen the inner workings of Repeated Measures ANOVA.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14