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In hierarchical multiple regression (not to be confused with hierarchical linear models that account for variance components), you add model terms by block. The fit of the new model is measured by the difference in multiple R-squared values and an F-test involving the residual sum of squares of each model.

My question is: Why do papers report the difference in multiple R-squared values instead of the difference in adjusted R-squared values? The F-test is not directly testing the difference between R-squared values. Furthermore, the adjusted R-squared accounts for the bias in multiple R-squared estimates. All this considered, why are people reporting multiple R-squared values?

Thanks in advance.

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    $\begingroup$ Welcome to Cross Validates! A cynic might say that it’s because adjusted $R^2$ is lower than $R^2$ (or at least not higher). $\endgroup$
    – Dave
    Commented Oct 8, 2023 at 22:06
  • $\begingroup$ Thank you, Dave! I don't think that should be a problem though. It could lead to misleading results, if anything. I don't really believe in this method, but most people in the social sciences prefer this over all other model selection methods so I don't have any choice but to understand why. $\endgroup$
    – Migs F
    Commented Oct 8, 2023 at 22:09

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I would say that it's because difference in $R^2$ has a very clear interpretation: "How much more of the variance is accounted for by the more complicated model?" A good statistician will then weigh that improvement against the added complexity.

Adjusted $R^2$, AFAIK, has no easy interpretation. It's an attempt to automate the judgment that the researcher uses in my first paragraph.

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  • $\begingroup$ Doesn't the adjusted $R^2$ correct for the bias when you include more variables to the model? $\endgroup$
    – Migs F
    Commented Oct 11, 2023 at 18:00
  • $\begingroup$ Yes. Or, at least, that's what it attempts to do. But it doesn't have an easy interpretation. $\endgroup$
    – Peter Flom
    Commented Oct 11, 2023 at 18:02

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