How to Interpret an Interaction in Two-Way ANOVA

Problem

When an interaction is significant, saying only "the teaching method worked" may be misleading because it may work only under certain conditions.

Who should use this

Use this when reading two-way ANOVA output, SPSS tables, or research result sections.

Formula and concept

Common interpretation order: interaction -> simple main effects -> main effects.

A main effect asks whether one factor differs overall. An interaction asks whether that difference depends on another factor. Significant interactions can hide or change main-effect interpretations.

Simple main effects examine differences within a specific level of another factor, such as comparing two teaching methods separately for lower and upper grades.

This page helps with calculation and reporting, but users should still confirm their research design, assumptions, and statistical interpretation.

Step by step

1. Check the interaction row first, such as method × grade.
2. If significant, inspect a means table or plot.
3. Run simple main effects or follow-up comparisons based on the research question.
4. Then describe main effects carefully as supporting context.

Worked example

Method A and B are compared across lower and upper grades. In lower grades, A = 78 and B = 77. In upper grades, A = 88 and B = 80. If the interaction is F(1, 76) = 5.90, p = .018, the method effect changes by grade, so grade-specific comparisons are needed.

Common mistakes

• Interpreting only main effects after a significant interaction.
• Drawing conclusions without cell means or a plot.
• Calling two significant main effects an interaction.
• Running many simple effects without a hypothesis or comparison control.

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