Factorial ANOVA

Like ANOVA but w. more factors/ IVs

e.g therapy type (2 options) & therapy setting (2 options) → 2×2 design

side is marginal means (simple effect)

H01: 𝜇1. = 𝜇2. - main effect of factor A


H02: 𝜇.1 = 𝜇.2 - main effect of factor B

H03: (𝜇11 - 𝜇12) = (𝜇21 - 𝜇22) - interaction effect

Graph examples

    No main effect of treatment condition bc if we disregard age both conditions are     equal (same/no slope)

    Main effect of age bc old always score higher than young (position on Y axis)

    No interaction bc lvl of col. is the same (lines are parallel)

    Main effect of treatment bc regardless of age, treatment A has lower lvl than gr. B

    Main effect of age bc old > young

    Yes interaction bc effect of treatment is different across age groups

    No main effect of treatment bc means of treat. A and B are equal

    No age effect bc not one group consistently scores higher

    Yes interaction

RQs

Main effect condition A: Is X the same across all lvl of A?

Main effect B: Is X the same for all lvl of B?

Interaction: Are the differences bet A the same for all of B?

Steps

  1. Check assumptions (normal distribution, homogeneity of var.)

  2. Check significance main effects and interaction (F-tests)

  3. If interaction is significant → make interaction plot // If not sign → remove interaction and rerun mode (NOTE: never include interaction w/o main effects)

    APA: The interaction bet. A and B was (not) found to be significant, F(df, df) = …, p = … . (After removal of the interaction term, both main effect were found significant)

  4. Determine effect size (partial eta equared 𝜂2𝑝)

    APA: The difference bet. A was significant, F(df, df) = …, p =…, 𝜂2𝑝 = …, indicating a … effect. The difference bet B was …

  5. Do post-hoc comparisons

    APA: Post-hoc tests revealed a significant difference bet. conditions C and D (p = …) and … . The difference bet. E and F was not significant (p = …)

  6. Simple main effects - test dif. of 1 factor within other factor

       APA: Simple main effects were significant for A1 (p = … ) and A2 (p = … ) //         The mean scores for A1 differ significantly (p = … )

  1. Report

       APA: (interaction) The difference between private (M = 7.74, SD = 1.16) and public (M = 6.76, SD = 1.48) companies was significant, F(1, 76) = 13.13, p = .001, , 𝜂2𝑝 = .147, indicating a medium effect. The differences between the three experimental conditions (policies) were significant, F(2, 76) = 8.09, p = .001, 𝜂2𝑝 = .176, indicating a medium large effect.

        Post-hoc tests revealed a significant difference between the experimental conditions “Free Lunch but working from office” and “Flexible Home days” (p = .017) and between the experimental condition “Free Lunch but working form office” and the control group (p < .001). The difference between the experimental condition “Flexible Home days” and the control group was not significant (p =.975). Simple main effects were significant for both private (p = .018) and public (p = .021) companies.

Bayesian

Model 1 (null) condition + type

Model 2 - interaction

The model without the interaction effect has about 5 times more support in the data than the one with (BF01 = …)