Slide 1

Slide 2

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

Slide 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.

Slide 4

For main effects, request follow ups for IVs 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

Slide 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

Slide 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

Slide 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.

Slide 8

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

Slide 9

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

Slide 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.

Slide 11

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

Slide 12

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

Slide 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.

Slide 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.

Slide 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

Slide 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.

Slide 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 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 to interpret significance Done. no yesAdjust DV and try again