# Two-Way ANOVA Tutorial: What to Do with a Significant Interaction?

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ANOVA f test Sum of Squares

We discussed how to conduct a 2-way factorial ANOVA in this tutorial, and we talked about the three different types of Sum of Squares here. We will build on these and discuss how to run post hoc analyses when you have a significant interaction. We will use the Moore dataset from the carData package in R. This data frame consists of subjects in a “social-psychological experiment who were faced with manipulated disagreement from a partner of either of low or high status. The subjects could either conform to the partner’s judgment or stick with their own judgment.” (John Fox, Sanford Weisberg and Brad Price (2018). carData: Companion to Applied Regression Data Sets. R package version 3.0-2. https://CRAN.R-project.org/package=carData)

The variables we will use in our analyses are:

• partner.status: Partner’s status. A factor with levels high and low.
• fcategory: F-Scale Categorized. A factor with levels low, medium, and high.
• conformity (outcome): Number of conforming responses in 40 critical trials.

First, we visualize the data. The following boxplot shows the distribution of scores on the conformity variable within each combination of partner.status and fcategory.