Two-way ANOVA A two way ANOVA is when we are testing the main ...

Two-way ANOVA A two way ANOVA is when we are testing the main effects of two variables on the DV, as well as if there are any simple main effects of one variable on another. AKA three comparisons are made: Main effects – overall, does one variable have an effect on the DV? Test TWO main effects in a 2x2 design. (e.g. is there a difference in confidence scores for control vs. Sleep deprived groups?) Simple main effects – does this have an effect on this specific thing? Looking at one variable at each level of the other. (e.g. overall, is there a difference in confidence scores for the groups given coffee vs the groups given the placebo?). Once we account for A and B variance, all that's left is the AxB interaction. SStotal (Variance)

Between Groups Variance

Effect B Variance

Effect A Variance

Within Groups Variance

AxB Interaction

In the example of Caffeine level (caffeine or placebo) vs Sleep status (control or sleep deprived), it is a 2x2 experimental design, meaning there are 4 experimental conditions (caffeine & control; caffeine & sleep deprived; placebo & control; placebo & sleep deprived), as shown below in the table. Cell means Caffeine level (B) (average of raw data) for Sleep status b1 b2 each group caffeine placebo (A) Marginal means for sleep status a1 control 4.0 3.9 3.95 Grand a2 sleep dep 3.7 2.2 2.95 mean 3.85

3.05

3.45

Marginal means for caffeine intake

Cell means are used to examine the interaction, whereas marginal means are used to examine the main effects of the variables.