Demystifying Statistical Analysis 3: The One-Way ANOVA Expressed in Linear Regression

In the previous part of this series, we looked at how the independent t-test can be expressed in a linear regression. The independent t-test is used when comparison is made between 2 unrelated groups, but what happens when we want to compare across more than 2 groups? In such a situation, the one-way ANOVA is the statistical analysis of choice. Just like the independent t-test, the one-way ANOVA involve the use of categorical predictors, and can be expressed in a linear regression.

For those who are unfamiliar with the one-way ANOVA and just want to know how it is usually conducted in SPSS, Laerd Statistics provides a comprehensive step-by-step guide. Otherwise, I will be explaining about the test using the following regression equation, with the help of the textbook “Data Analysis: A Model Comparison Approach” by Carey Ryan, Charles M. Judd, and Gary H. McClelland:

Ŷi = b0 + b1X1i + b2X2i

When comparing more than 2 groups, (m — 1) coded predictors are required in the regression model, where m is the number of groups. In the case of 3 groups, 2 additional parameters b1 and b2 need to be estimated, on top of the intercept b0.

Just as in the independent t-test, dummy coding can be used, but a fixed reference group needs to be selected, where it is coded as 0 for all the constructed predictors. In the case of a categorical predictor that is ordinal (ranked), selecting the lowest…