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Within Subject ANOVAs: Assumptions & Post Hoc Tests

Within Subject ANOVAs: Assumptions & Post Hoc Tests. Outline of Today’s Discussion. Within Subject ANOVAs in SPSS Within Subject ANOVAs: Assumptions & Post Hoc Tests In Class Exercise: Applying our knowledge to 200-level Research Courses. The Research Cycle. Real World. Research

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Within Subject ANOVAs: Assumptions & Post Hoc Tests

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  1. Within Subject ANOVAs:Assumptions &Post Hoc Tests

  2. Outline of Today’s Discussion • Within Subject ANOVAs in SPSS • Within Subject ANOVAs: Assumptions & Post Hoc Tests • In Class Exercise: Applying our knowledge to 200-level Research Courses

  3. The Research Cycle Real World Research Representation Abstraction Generalization Methodology *** Data Analysis Research Results Research Conclusions

  4. Part 1 Within Subject ANOVAs in SPSS

  5. Within Subject ANOVAs in SPSS • Fun Fact: It can be shown that there is a formal mathematical relationship between ANOVA and linear correlations! • Any ANOVA is considered a special case of a “linear model”, to mathematicians. (We won’t bother with the details here.) • Here are the SPSS steps for the within-subjects ANOVA: Analyze  General Linear Model  Repeated Measures

  6. Within Subject ANOVAs in SPSS • You will then be prompted by a box… “Repeated Measures Define Factor(s)” • For each variable in your ANOVA, you will be prompted for a Factor Name (of your choosing), and the number of levels. • You can click ADD after each variable is entered…then click DEFINE….

  7. Within Subject ANOVAs in SPSS • Finally, you should slide the variables in the left box over to the “Within-Subjects Variables” box on the right. • Note: SPSS does NOT conduct Post Hoc tests on Within Subjects variables. (Say it with me)

  8. Part 2 Within Subject ANOVAs: Assumptions & Post Hocs

  9. 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.)

  10. Assumptions & Post Hocs The repeated measures ANOVA is based on the “Sphericity Assumption” (say it with me)

  11. 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!

  12. 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.

  13. Assumptions & Post Hocs Within-Subjects ANOVA Because this “Sig.” value is < 0.05, we “reject something”! …namely, the sphericity assumption.

  14. 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”….

  15. Assumptions & Post Hocs Within-Subjects ANOVA If we retain the sphericity assumption, use the df an F values in the top row(s).

  16. Assumptions & Post Hocs Within-Subjects ANOVA If we reject the sphericity assumption, use the “Greenhouse-Geisser” row(s)…

  17. Assumptions & Post Hocs Within-Subjects ANOVA When sphericity is not assumed, the degrees of freedom are adjusted according to these epsilon values (coefficients).

  18. Assumptions & Post Hocs Within-Subjects ANOVA Could someone walk us through the relationship between the DF & epsilon values here?

  19. 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. :( ……

  20. 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?

  21. Assumptions & Post Hocs • The Bonferronipost 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.

  22. 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?

  23. 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?

  24. 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?

  25. 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?

  26. 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?

  27. Part 3 In Class Exercise: Applying Our Methods To 200-Level Research Courses

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