Week 4 short PSY 311: Two-Factor ANOVA Study Notes

Two-Factor ANOVA

Overview of ANOVA

  • One-way ANOVA: examines one independent variable with multiple levels.

  • Two-way ANOVA: involves two independent variables (Factors A and B), each can have multiple levels.

  • Written as an a x b design, assessing interactions affecting the dependent variable.

Objectives

  • Design a two-way ANOVA.

  • Input data into jamovi.

  • Use Linear Models module for analysis.

  • Interpret and report jamovi output.

  • Understand interactions and conduct multiple comparisons (e.g., Bonferroni adjustments).

Theory of Two-Way ANOVA

  • Allows investigation of:

    • Main effects of each independent variable.

    • Interaction effects between the two independent variables.

Main Effects and Interactions

  • Main effect of Age: overall impact on recall (averaging over conditions).

  • Main effect of Condition: overall impact on recall (averaging over age).

  • Interaction: checks if the effect of one variable changes at different levels of the other variable.

ANOVA Model (Two-Way)

  • Score = Grand Mean + Treatment effect of IV A + Treatment effect of IV B + Interaction effect + Residual error.

  • Mathematical representation: X{ijk} = ext{μ} + ai + bj + ab{ij} + e_{ijk}.

Hypotheses in Two-Way ANOVA

  1. Equal marginal means for IV A.

  2. Equal marginal means for IV B.

  3. No interaction effect between IV A and IV B.

Summary Table for Two-Factor ANOVA

  • Three F-tests for main effects and interaction:

    • Main effect of A: F(a-1, ab(n-1)).

    • Main effect of B: F(b-1, ab(n-1)).

    • Interaction effect: F((a-1)(b-1), ab(n-1)).

Outcome Interpretation

  • All three are significant tests can require post-hoc tests if conditions exceed two levels.

  • Interaction effect overrides main effects if significant.

Running Analysis in jamovi

  • Data Entry:

    • One column for each IV and one for the DV (participants per row).

  • Test assumptions (homogeneity), evaluate main effects, and plot results.

Post-Hoc Tests and Reporting

  • For significant main effects with multiple levels, conduct follow-up tests (e.g., Tukey, Bonferroni).

  • Write-up example includes F-values, p-values, means, and standard deviations.

Understanding Two-Way Interaction

  • Tests simple main effects after a significant interaction.

  • Analyze each level of one factor at each level of the second factor.

Effect Size in Factorial Designs

  • Use partial eta squared as a measure of effect size:

    • Ranges from 0 to 1 (small: 0.01, medium: 0.06, large: 0.14).

Key Points

  • Two-way ANOVA tests:

    • Main effects of each independent variable.

    • Interaction effect qualifies main effects.

    • Avoid Type I errors with adjustments for multiple comparisons.