within subject anovas: assumptions & post hoc tests
DESCRIPTION
The Research Cycle Real World Research Representation Research Results Research Conclusions Abstraction Data Analysis MethodologyGeneralization ***TRANSCRIPT
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Within Subject ANOVAs:Assumptions
&Post Hoc Tests
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Outline of Today’s Discussion
1. Within Subject ANOVAs in SPSS
2. Within Subject ANOVAs: Assumptions & Post Hoc Tests
3. In Class Exercise: Applying our knowledge to 200-level Research Courses
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The Research Cycle
Real World
ResearchRepresentation
ResearchResults
ResearchConclusions
Abstraction
Data Analysis
MethodologyGeneralization
***
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Part 1
Within Subject ANOVAs in SPSS
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Within Subject ANOVAs in SPSS
1. Fun Fact: It can be shown that there is a formal mathematical relationship between ANOVA and linear correlations!
2. Any ANOVA is considered a special case of a “linear model”, to mathematicians. (We won’t bother with the details here.)
3. Here are the SPSS steps for the within-subjects ANOVA:Analyze General Linear Model Repeated Measures
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Within Subject ANOVAs in SPSS
1. You will then be prompted by a box… “Repeated Measures Define Factor(s)”
2. For each variable in your ANOVA, you will be prompted for a Factor Name (of your choosing), and the number of levels.
3. You can click ADD after each variable is entered…then click DEFINE….
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Within Subject ANOVAs in SPSS
1. Finally, you should slide the variables in the left box over to the “Within-Subjects Variables” box on the right.
2. Note: SPSS does NOT conduct Post Hoc tests on Within Subjects variables.
(Say it with me)
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Part 2
Within Subject ANOVAs:Assumptions & Post Hocs
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Assumptions & Post Hocs
Between-Subjects ANOVA Equal Variance Assumption
The “Sig.” value here is > 0.05,so we retain the equal variance assumption.(The ANOVA is a fair test of this data set.)
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Assumptions & Post Hocs
The repeated measures ANOVA is based on the
“Sphericity Assumption”(say it with me)
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Assumptions & Post Hocs• Sphericity Assumption - The correlations among
scores in the various conditions are equal (or close enough!).
• Correlation between A & B, is equal to the correlation between A & C, which is equal to the correlation between B & C, etc..
• The sphericity assumption is a bit more complicated than that, but that will do!
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Assumptions & Post Hocs• Great News!
• SPSS automatically conducts a test (Mauchly’s Test of Sphericity) to indicate whether the sphericity assumption should be retained or rejected.
• Remember: SPSS did the same for us in the between-subjects case with Levene’s statistic.
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Assumptions & Post Hocs
Within-Subjects ANOVA
Because this “Sig.” value is < 0.05,we “reject something”!
…namely, the sphericity assumption.
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Assumptions & Post Hocs
Within-Subjects ANOVA
If this “Sig.” value had been >0.05,we could use the F-Value listed in the row labeled “Sphericity Assumed”….
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Assumptions & Post Hocs
Within-Subjects ANOVA
If we retain the sphericity assumption,use the df an F values in the top row(s).
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Assumptions & Post Hocs
Within-Subjects ANOVA
If we reject the sphericity assumption,use the “Greenhouse-Geisser” row(s)…
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Assumptions & Post Hocs
Within-Subjects ANOVA
When sphericity is not assumed,the degrees of freedom are adjusted according to
these epsilon values (coefficients).
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Assumptions & Post Hocs
Within-Subjects ANOVA
Could someone walk us through therelationship between the DF & epsilon values here?
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Assumptions & Post Hocs
• Review Question: What were the two reasons for using post hoc tests?
• Unfortunately, SPSS does not perform post hoc tests for the within-subjects ANOVAs. :( ……
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Assumptions & Post Hocs
• To isolate which means differ from which in a within-subjects ANOVA, we can use “lots of little” repeated measures t-tests.
• Of course, this raises the problem of cumulative type 1 error.
• What was cumulative type 1 error, again?
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Assumptions & Post Hocs• The Bonferroni post hoc adjustment controls cumulative type 1
error among the repeated measures t-tests by multiplying each observed alpha level (“sig” value) by the number of t-tests we’ve run.
• Example: If we run 2 t-tests (post hoc), we would multiply each observed alpha level (“sig” value) by 2, and compare it to 0.05 (as always).
• Now, the new Bonferroni-adjusted ‘sig’ value for a particular t-test in SPSS would have to be lower than 0.05 for us to claim statistical significance.
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Assumptions & Post Hocs
• Let’s get some practice with this idea.
• Let’s say we ran 5 t-tests (post hoc).
• If a particular t-test had a “sig” value of 0.015, would we retain or reject?
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Assumptions & Post Hocs
• Let’s get some practice with this idea.
• Let’s say we ran 4 t-tests (post hoc).
• If a particular t-test had a “sig” value of 0.015, would we retain or reject?
![Page 24: Within Subject ANOVAs: Assumptions & Post Hoc Tests](https://reader035.vdocument.in/reader035/viewer/2022062317/5a4d1b547f8b9ab0599a8cd8/html5/thumbnails/24.jpg)
Assumptions & Post Hocs
• Let’s get some practice with this idea.
• Let’s say we ran 3 t-tests (post hoc).
• If a particular t-test had a “sig” value of 0.015, would we retain or reject?
![Page 25: Within Subject ANOVAs: Assumptions & Post Hoc Tests](https://reader035.vdocument.in/reader035/viewer/2022062317/5a4d1b547f8b9ab0599a8cd8/html5/thumbnails/25.jpg)
Assumptions & Post Hocs
• Let’s get some practice with this idea.
• Let’s say we ran 2 t-tests (post hoc).
• If a particular t-test had a “sig” value of 0.04, would we retain or reject?
![Page 26: Within Subject ANOVAs: Assumptions & Post Hoc Tests](https://reader035.vdocument.in/reader035/viewer/2022062317/5a4d1b547f8b9ab0599a8cd8/html5/thumbnails/26.jpg)
Assumptions & Post Hocs
• Let’s get some practice with this idea.
• Let’s say we ran 2 t-tests (post hoc).
• If a particular t-test had a “sig” value of 0.015, would we retain or reject?
![Page 27: Within Subject ANOVAs: Assumptions & Post Hoc Tests](https://reader035.vdocument.in/reader035/viewer/2022062317/5a4d1b547f8b9ab0599a8cd8/html5/thumbnails/27.jpg)
Part 3
In Class Exercise:Applying Our Methods
To 200-Level Research Courses
![Page 28: Within Subject ANOVAs: Assumptions & Post Hoc Tests](https://reader035.vdocument.in/reader035/viewer/2022062317/5a4d1b547f8b9ab0599a8cd8/html5/thumbnails/28.jpg)