Chapter 14: Two-Factor Analysis of Variance (Independent Measures)

Two-Way ANOVA has ______ independent variables.

two

Two-Way ANOVA evaluates _______ sets of mean differences

three

Two-Way ANOVA has ______ hypothesis tests in one analysis

three

Hypothesis test in two-way ANOVA are _______?

Independent

For hypothesis test there is factor ____.

A&B

NULL HYPOTHESIS

There is no interaction between factors A and B. All of the mean differences between groups are explained by the main effects of
the two factors.

μ𝐴1 = μ𝐴2, μB1 = μB2

ALTERNATIVE HYPOTHESIS

There is an interaction between factors The mean differences between groups are not what would be predicted from the overall main effects of the two factors.

𝐻1: μ𝐴1 ≠ μ𝐴2, 𝐻1: μB1 ≠ μB2

STAGE 1

SAME AS ONE-WAY ANOVA

STAGE 2

Break down between-group variability

In an A X B interaction the “extra“ mean differences not accounted for by the main effects of the two factors.

________ will be the denominator for all 3 F-ratios

will be the denominator for all 3 F-ratios

Critical F-ration values

• Different critical F-ratio for each calculated F-ratio

• Use the df for each calculated F-ratio

Effect Size

• Criteria is the same! (0.10, 0.25, 0.40)

• Calculate η2 separately for each of the 3 comparisons

• Remove any variability that can be explained by
  other sources