r2 and R2

Dear Students,

Over the weekend, Carol sent me a brief but interesting question. She indicated that while looking at a research article for another class, she came across the notation "R2." Carol's question to me was short and clear. "Does R2," she asked, "mean the same thing as the r2 that we've discussed in class?"

Because others of you may have had the same question (about r2 and R2) as you've read research reports, I thought you might like to see how I responded to Carol's question.

Sky Huck

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Dear Carol,

You've asked a very good question. If you'll stick with me for about 60 seconds, I think I can point out how r2 and R2 are similar and how they are different.

R2 is conceptually the same as r2. In other words, each one is a "coefficient of determination," indicating the extent to which variables are related. In both cases, when this coefficient is multiplied by 100, we get the percentage of "shared variance."

The difference between r2 and R2 concerns the number of variables that were focused on by the researcher. If you see r2, it's a good bet that there were only 2 variables being correlated. On the other hand, if you see R2, it's highly likely that the the researcher was dealing with 3 or more variables. In this latter situation, the researcher was probably trying to assess the degree to which variability among the scores on one particular variable could be explained by a combination of the other variables. For example, a researcher might collect data on weight loss, caloric intake, and amount of exercise, and then he/she might analyze the data to see if variability in weight loss is associated with (or can be "explained by") variability in caloric intake and exercise.

When there are 3 or more variables involved, as in the example I've just given, researchers usually say that they have conducted (or intend to conduct) a "multiple regression." One of the key concepts in multiple regression is R2, just as r2 is a concept in bivariate correlation.

If you'd like to learn a bit more about R2 and multiple regression, take a look at the middle third of Chapter 19 (pp. 579-589). That portion of the book focuses on multiple regression's goals, needed data, results, and limitations. In Excerpts 19.20-19.24, you'll see examples of R2 (and some closely related variants of R2).

I hope this explanation helps.

Sky Huck

Copyright © 2012

Schuyler W. Huck
All rights reserved.

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