Interaction
b. If there does appear to be an interaction between gender and age bracket, how should we continue with the procedure for two-way analysis of variance?

Verified step by step guidance

1. Understand that in a two-way ANOVA, an interaction between two factors (here, gender and age bracket) means the effect of one factor depends on the level of the other factor.
2. If an interaction is present, the main effects of gender and age bracket should not be interpreted in isolation because the combined effect influences the response variable.
3. Proceed by examining the simple effects, which means analyzing the effect of one factor at each level of the other factor separately. For example, analyze the effect of gender within each age bracket, and vice versa.
4. Use post hoc tests or multiple comparisons within each subgroup to identify where significant differences lie, since the interaction suggests that the differences vary across groups.
5. Report the interaction effect clearly and focus your conclusions on how the factors jointly influence the outcome, rather than only on the main effects.

Key Concepts

Interaction Effect in Two-Way ANOVA

An interaction effect occurs when the effect of one factor (e.g., gender) on the response variable depends on the level of another factor (e.g., age bracket). Detecting interaction means the factors do not operate independently, and their combined influence must be considered in the analysis.

Two-Way ANOVA Procedure with Interaction

When an interaction is present, the two-way ANOVA procedure involves analyzing both main effects and the interaction effect simultaneously. The interaction term is tested first, and if significant, interpretation focuses on the interaction rather than main effects alone.

Post Hoc Analysis and Simple Effects

If interaction is significant, follow-up analyses such as simple effects tests or post hoc comparisons are conducted to explore differences within specific factor combinations. This helps clarify how the factors jointly influence the outcome across different groups.