ANOVA > ANOVA vs Regression
If you’re working on data analysis, there are many tools available to provide insights to your data. These tools include ANOVA and regression analysis. At first glance, the two methods may look similar—so similar in fact, that you wouldn’t be the first to completely confuse the two.
ANOVA vs Regression: Key Similarities
ANOVA can be described as “Analysis of variance approach to regression analysis” (Akman), although ANOVA can be reserved for more complex regression analysis (Akman, n.d.).
Both result in continuous output (Y) variables. And both can have continuous variables as (X) inputs—or categorical variables. If you use exactly the same structure for both tests (see the demonstration of dummy coding here for an example), they are effectively the same; In fact, ANOVA is a “special case” of multilevel regression.
ANOVA vs Regression: Key Differences
ANOVA can provide one piece of information that regression cannot: structure on the regression coefficients (Andrew, 2019).
The preferred inputs for ANOVA are categorical variables. You can think of ANOVA as a regression with a categorical predictors (Pruim, n.d.). However, you can choose to use continuous variables. The opposite is true: use continuous variables for regression with categorical variables as a second option. The reason that categorical variables are a second option in regression analysis is that you can’t just plug in categorical data into your regression model; You have to code dummy variables first. Dummy coding is where you give your categorical variables a numeric value, like “1” for black and “0” for white.
Akman, O. RATS: ANOVA. Retrieved July 13, 2020 from: http://my.ilstu.edu/~oakman/RAO/anova.htm
Andrew (2019). Understanding how Anova relates to regression. Retrieved July 13, 2020 from: https://statmodeling.stat.columbia.edu/2019/03/28/understanding-how-anova-relates-to-regression/
Prium, R. (n.d.). 1-Way ANOVA. Retrieved July 13, 2020 from: https://www.calvin.edu/~rpruim/courses/m143/F10/fromClass/AnovaSlides/anova-handout-4x.pdf
Vik, P. (2013). Regression, ANOVA, and the General Linear Model: A Statistics Primer 1st Edition. SAGE.