2. Factorial Analysis of Variance II Follow up tests More fun than a rub down with a cheese grater 1.

3. KNR 445 FACTORIAL ANOVA II Slide 2 Follow-ups for Factorial ANOVA  Recall possible outcomes from Factorial ANOVA:  Main effects  Interactions  What might be missing (not specified) from these results?  Differences between pairs of means within each factor (if levels of factor are > 2)  Differences between cells giving rise to interactions 1. 2.

4.  For main effects, request follow ups for IV’s with > 2 levels KNR 445 FACTORIAL ANOVA II Slide 3 Follow-ups for Main Effects 2. 1. “Post Hoc” lets you request follow- ups, but only to the main effects

5. KNR 445 FACTORIAL ANOVA II Slide 4 Follow-ups for Main Effects To do a post hoc on the main effects: 1. select the variables 2. Slide them over 4. Continue 3. Select the post hoc test

6. KNR 445 FACTORIAL ANOVA II Slide 5 Follow-ups for Interactions  What is an interaction?  Arises from the cell means/SDs  Significant non-parallelism 1. 2. 4. 3. Pressure Level Low Pressure Moderate pressure High Pressure Anxiety Level Low Anxiety M = 5 (3, 7) M = 8 (7, 9) M = 11 (10, 12) M A1 = 8 High Anxiety M = 4 (3, 5) M = 6 (5, 7) M = 2 (2, 2) M A2 = 4 M B1 = 4.5M B2 = 7M B3 = 6.5M total = 12

7. In our example, this would be looking for differences in performance associated with pressure level, within each anxiety level Pressure Level Low Pressure Moderate pressure High Pressure Anxiety Level Low Anxiety M = 5 (3, 7) M = 8 (7, 9) M = 11 (10, 12) High Anxiety M = 4 (3, 5) M = 6 (5, 7) M = 2 (2, 2)  Subsequent simpler analyses  These can go in at least a couple of directions  With a 3 x 2 ANOVA, you could do:  2 one-way ANOVAs (one at each level of the IV w/2 levels)  One 1-way ANOVA on low anxiety  One 1-way ANOVA on high KNR 445 FACTORIAL ANOVA II Slide 6 Follow-ups for Interactions 1. 2. 4. 3. 5.

8. KNR 445 FACTORIAL ANOVA II Slide 7 Follow-ups for Interactions 1. 2. 3.

9. KNR 445 FACTORIAL ANOVA II Slide 8 Follow-ups for Interactions 1. 2.

10. KNR 445 FACTORIAL ANOVA II Slide 9 Follow-ups for Interactions  Subsequent simpler analyses  Second possibility:  3 t-tests (one at each level of the IV w/3 levels)  In our example, this would be looking for differences in performance associated with anxiety level, within each pressure level  One for low pressure  One for moderate pressure  One for high pressure 1. 2.

11. KNR 445 FACTORIAL ANOVA II Slide 10 Follow-ups for Interactions 1.

12. KNR 445 FACTORIAL ANOVA II Slide 11 Follow-ups for Interactions 1.

13. KNR 445 FACTORIAL ANOVA II Slide 12 Follow-ups for Interactions  Final step – control for type 1 error :  Because you are now conducting multiple tests, you should adjust your significance threshold to control for type 1 error.  The Bonferroni adjustment is suitable here  divide  by the number of tests being run  So for 2 1-way ANOVAs, use  =.05/2 =.025  For 3 independent t-tests, use  =.05/3 =.017 1.

14. KNR 445 FACTORIAL ANOVA II Slide 13 Follow-ups for Interactions  Follow-ups on significant interactions :  Bear in mind that any test conducted after the initial interaction is less powerful than the initial test  So sometimes you will get no significance from the follow-up despite a significant initial test  In this instance, all you can do is suggest cautiously where the differences lie, “by inspection” 1.

15. KNR 445 FACTORIAL ANOVA II Slide 14 Follow-ups for Interactions  Follow-ups on significant interactions :  Note on ordinal (uncrossed) and disordinal (crossed) interactions  Regardless of whether the interaction crosses or not, there is a good chance that main effects found in these analyses are not genuine (that is their existence depends on the level of the other factor)  Always interpret a main effect with caution if there is a significant interaction involving that main effect 1. 2. Uncrossed – genuine main effect 4. Crossed – no genuine main effect 3. Uncrossed – no genuine main effect

16. KNR 445 FACTORIAL ANOVA II Slide 15 Follow-ups for Factorial ANOVA  Summary  No significant effects -No follow ups  Significant main effect only  Pairwise comparisons within significant effects  Significant main effects and a significant interaction  Caution in interpreting main effects (examine graph of interaction)…may be superseded by interaction  Try to find the locus of the interaction (by further ANOVAs and t-tests with Bonferroni adjustment)  Significant interaction only 1.

17. main effect(s) and interaction (Partial) Flow chart for Factorial ANOVA KNR 445 FACTORIAL ANOVA Slide 16 Run ANOVA Is homogeneity significant? 1 1.Include homogeneity tests; descriptives; partial η 2 ; request post-hocs if appropriate, and PLOT of interaction. Are there any significant effects? no Stop! yes What are they? Only main effects Only interaction Use post-hocs to interpret – like t-tests 1. Use post-hocs to interpret main effects, BUT consider plot of interaction to see if genuine. 2. Split file by one variable and run either t-tests or 1-way ANOVA on other to examine locus of interaction 3. Use adjusted α to interpret significance Done. no yesAdjust DV and try again