Interaction Effects

Statistics · Axiom Academy

Understanding how factors combine in two-way ANOVA 1 What is an Interaction Effect? Suppose we study the effect of study method (reading vs. practice problems) and time of day (morning vs. evening) on test scores. An interaction would mean that the best study method depends on the time of day—perhaps reading works better in the morning, while practice problems work better in the evening. 2 Visualizing Interactions with Interaction Plots No Interaction: The effect of Factor A is the same regardless of Factor B level (parallel lines) Interaction Present: The effect of Factor A changes depending on Factor B level (crossing lines) 3 Testing for Interaction: The F-test MS AB = Mean square for interaction = SS AB / df AB MS Error = Mean square error (within-groups variability) df AB = (a - 1)(b - 1), where a and b are the number of levels 4 Interpreting Significant Interactions Suppose we find a significant interaction between drug treatment and exercise on blood pressure reduction: With Exercise: Drug A reduces BP by 20 points, Drug B by 25 points Without Exercise: Drug A reduces BP by 15 points, Drug B by 10 points Interpretation: We cannot simply say "Drug B is more effective." The effectiveness depends on exercise—Drug B is better with exercise, but Drug A is better without exercise.

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