One-Way Analysis of Variance

Factorial Analysis of Variance IIFollow up testsMore fun than a rub down with a cheese grater1.

KNR 445FACTORIALANOVA IISlide 2Follow-ups for Factorial ANOVARecall possible outcomes from Factorial ANOVA:Main effectsInteractionsWhat 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 interactions1. 2.

For main effects, request follow ups for IVs with > 2 levelsKNR 445FACTORIALANOVA IISlide 3Follow-ups for Main Effects2.

1. Post Hoc lets you request follow-ups, but only to the main effects

KNR 445FACTORIALANOVA IISlide 4Follow-ups for Main EffectsTo do a post hoc on the main effects: 1. select the variables2. Slide them over4. Continue3. Select the post hoc test

KNR 445FACTORIALANOVA IISlide 5Follow-ups for InteractionsWhat is an interaction?Arises from the cell means/SDsSignificant non-parallelism1. 2. 4. 3. Pressure LevelLow PressureModerate pressureHigh PressureAnxiety LevelLow AnxietyM = 5(3, 7)M = 8(7, 9)M = 11(10, 12)MA1 = 8High AnxietyM = 4(3, 5)M = 6(5, 7)M = 2(2, 2)MA2 = 4

MB1 = 4.5MB2 = 7MB3 = 6.5Mtotal = 12

In our example, this would be looking for differences in performance associated with pressure level, within each anxiety levelPressure LevelLow PressureModerate pressureHigh PressureAnxiety LevelLow AnxietyM = 5(3, 7)M = 8(7, 9)M = 11(10, 12)High AnxietyM = 4(3, 5)M = 6(5, 7)M = 2(2, 2)Subsequent simpler analysesThese can go in at least a couple of directionsWith 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 highKNR 445FACTORIALANOVA IISlide 6Follow-ups for Interactions1. 2. 4. 3.

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KNR 445FACTORIALANOVA IISlide 7Follow-ups for Interactions1.

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KNR 445FACTORIALANOVA IISlide 8Follow-ups for Interactions

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KNR 445FACTORIALANOVA IISlide 9Follow-ups for InteractionsSubsequent simpler analysesSecond 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 levelOne for low pressureOne for moderate pressureOne for high pressure1. 2.

KNR 445FACTORIALANOVA IISlide 10Follow-ups for Interactions

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KNR 445FACTORIALANOVA IISlide 11Follow-ups for Interactions1.

11KNR 445FACTORIALANOVA IISlide 12Follow-ups for InteractionsFinal 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 heredivide by the number of tests being run So for 2 1-way ANOVAs, use = .05/2 = .025For 3 independent t-tests, use = .05/3 = .0171.

KNR 445FACTORIALANOVA IISlide 13Follow-ups for InteractionsFollow-ups on significant interactions :Bear in mind that any test conducted after the initial interaction is less powerful than the initial testSo sometimes you will get no significance from the follow-up despite a significant initial testIn this instance, all you can do is suggest cautiously where the differences lie, by inspection1.

KNR 445FACTORIALANOVA IISlide 14Follow-ups for InteractionsFollow-ups on significant interactions :Note on ordinal (uncrossed) and disordinal (crossed) interactionsRegardless 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 effect4. Crossed no genuine main effect3. Uncrossed no genuine main effect

KNR 445FACTORIALANOVA IISlide 15Follow-ups for Factorial ANOVASummaryNo significant effects -No follow upsSignificant main effect onlyPairwise comparisons within significant effectsSignificant main effects and a significant interactionCaution in interpreting main effects (examine graph of interaction)may be superseded by interactionTry to find the locus of the interaction (by further ANOVAs and t-tests with Bonferroni adjustment)Significant interaction only1.

main effect(s) and interaction(Partial) Flow chart for Factorial ANOVAKNR 445FACTORIALANOVASlide 16Run ANOVAIs homogeneity significant?1Include homogeneity tests; descriptives; partial 2; request post-hocs if appropriate, and PLOT of interaction. Are there any significant effects?noStop!yesWhat are they?Only main effectsOnly interactionUse post-hocs to interpret like t-tests1. 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 interaction3. Use adjusted to interpret significanceDone.noyesAdjust DV and try again