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Page 1: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 2: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Basics of parametric statistics ANOVA – Analysis of Variance T-Test and ANOVA in SPSS

Lunch

T-test in SPSS ANOVA in SPSS

Page 3: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 4: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

The arithmetic mean can only be derived from interval or ratio measurements.

Interval data – equal intervals on a scale; intervals between different points on a scale represent the difference between all points on the scale.

Ratio Data – has the same property as interval data, however the ratios must make mutually sense. Example 40 degrees is not twice as hot as 20 degrees; reason the celsius scale does not have an absolute zero.

Page 5: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Assumption 1:Homogeneity of variance – means should be equally accurate.

Assumption 2:In repeated measure designs: Sphericity assumption.

Assumption 3: Normal Distribution

Page 6: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Assumption 1:Homogeneity of variance

The spread of scores in each sample should be roughly similar

Tested using Levene´s test

Assumption 2:The sphericity assumption

Tested using Mauchly´s test Basically the same thing: homogeneity of

variance

Page 7: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Assumption 3: Normal Distribution. In SPSS this can be checked by using:

▪ Kolmogorov-Smirnov test▪ Shapiro-Wilkes test

These compare a sample set of scores to a normally distributed set of scores with the same mean and standard deviation.

If (p> 0.05) The distribution is not significantly different from a normal distribution

If (p< 0.05) The distribution is significantly different from a normal distribution

Page 8: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 9: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Difference between t-test and ANOVA: t-test is used to analyze the difference

between TWO levels of an independent variable.

ANOVA is used to analyze the difference between MULTIPLE levels of an independent variable.

Page 10: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Independent variable = apple

Dependent variables could be: sweetness, decay time etc.

t-test ANOVA

…or more

Page 11: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

The ANOVA tests for an overall effect, not the specific differences between groups.

To find the specific differences use either planned comparisons or post hoc test. Planned comparisons are used when a

preceding assumptions about the results exists. Post Hoc analysis is done subsequent to data

collection and inspection.

Page 12: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

A Post Hoc Analysis is somewhat the same as doing a lot of t-tests with a low significance cut-of point, the Type I error is controlled at 5%. Type I error: Fisher’s criterion states that there is a

o.o5 probability that any significance is due to diversity in samples rather than the experimental manipulation – the α-level.

Using a Bonferroni correction adjusts the α-level according to number of tests done (2 test = o.5/2 = 0.025. 5 test= 0.5/5= 0.01). Basically the more tests you do the lower the cut of point.

Page 13: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Variation in a set of scores comes from two sources:

Random variation from the subjects themselves (due to individual variations in motivation, aptitude, etc.)

Systematic variation produced by the experimental manipulation.

Page 14: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

ANOVA compares the amount of systematic variation to the amount of random variation, to produce an F-ratio:

systematic variation

random variation (‘error’)F =

Page 15: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Large value of F: a lot of the overall variation in scores is due to the experimental manipulation, rather than to random variation between subjects.

Small value of F: the variation in scores produced by the experimental manipulation is small, compared to random variation between subjects.

Page 16: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

In practice, ANOVA is based on the variance of the scores. The variance is the standard deviation squared:

variance

(X X ) 2

N

Page 17: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

We want to take into account the number of subjects and number of groups. Therefore, we use only the top line of the variance formula (the "Sum of Squares", or "SS"):

We divide this by the appropriate "degrees of freedom" (usually the number of groups or subjects minus 1).

sum of squares

(X X ) 2

Page 18: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Between groups SSM: a measure of the amount of variation between the groups. (This is due to our experimental manipulation).

Page 19: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Within GroupsR: a measure of the amount of variation within the groups. (This cannot be due to our experimental manipulation, because we did the

same thing to everyone within each group).

Page 20: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Total sum of squares:a measure of the total amount of variation amongst all the scores. (Total SS) = (Between-groups SS) + (Within-groups SS)

Page 21: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

The bigger the F-ratio, the less likely it is to have arisen merely by chance.

Use the between-groups and within-groups d.f. to find the critical value of F.

Your F is significant if it is equal to or larger than the critical value in the table.

Page 22: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

1 2 3 4

1 161.4 199.5 215.7 224.6

2 18.51 19.00 19.16 19.25

3 10.13 9.55 9.28 9.12

4 7.71 6.94 6.59 6.39

5 6.61 5.79 5.41 5.19

6 5.99 5.14 4.76 4.53

7 5.59 4.74 4.35 4.12

8 5.32 4.46 4.07 3.84

9 5.12 4.26 3.86 3.63

10 4.96 4.10 3.71 3.48

11 4.84 3.98 3.59 3.36

12 4.75 3.89 3.49 3.26

13 4.67 3.81 3.41 3.18

14 4.60 3.74 3.34 3.11

15 4.54 3.68 3.29 3.06

16 4.49 3.63 3.24 3.01

17 4.45 3.20 3.20 2.96

Here, look up the critical F-value for 3 and 16 d.f.

Columns correspond to between-groups d.f.; rows correspond to within-groups d.f.

Here, go along 3 and down 16: critical F is at the intersection.

Our obtained F, 25.13, is bigger than 3.24; it is therefore significant at p<.05. (Actually it’s bigger than 9.01, the critical value for a p of 0.001).

Page 23: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

One –Way ANOVA Independent Repeated Measures

Two-way ANOVA Independent Mixed Repeated Measures

N-way ANOVA

Page 24: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

One-Way: ONE INDEPENDENT VARIABLE

Independent: 1 participant = 1 piece of data.

Independent variable: Yoga Pose,3 levels

Dependent variables: Heart rate, oxygen saturation

Page 25: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

One-Way: ONE INDEPENDENT VARIABLE

Dependent : 1 participant = Multiple pieces of data.

Independent variable:Cake,3 levels

Dependent variables: Blood sugar, pH-balance

Page 26: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Two-Way : TWO INDEPENDENT VARIABLES

Independent : 1 participant = 1 piece of data.

Independent variables: Age, Music Style

>40 <40

Indie-Rock Classic Pop

Page 27: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Two-Way : TWO INDEPENDENT VARIABLES

Mixed: Variable 1: Independent (Controller) Variable 2: Repeated measures (Space Ship)

Page 28: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Two-Way: TWO INDEPENDENT VARIABLES

Dependent : 1 participant = Multiple pieces of data.

Independent variables: Exercise, Temperature

20 ° 25 ° 30 °

Page 29: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 30: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 31: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 32: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Running SPSS (repeated measures t-test)

Page 33: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Running SPSS (repeated measures t-test)

Page 34: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Running SPSS (repeated measures t-test)

Page 35: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Interpreting SPSS output (repeated measures t-test)

Page 36: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 37: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

RUNNING SPSS

Page 38: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 39: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 40: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

Click ‘Options…’Then Click Boxes: Descriptive; Homogeneity of variance test; Means plot

Page 41: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

SPSS output

Page 42: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA
Page 43: ANOVA Analysis of Variance.  Basics of parametric statistics  ANOVA – Analysis of Variance  T-Test and ANOVA in SPSS  Lunch  T-test in SPSS  ANOVA

One-way independent-measures ANOVA enables comparisons between 3 or more groups that represent different levels of one independent variable.

A parametric test, so the data must be interval or ratio scores; be normally distributed; and show homogeneity of variance.

ANOVA avoids increasing the risk of a Type 1 error.