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Following my question here, when is it appropriate (or inappropriate) to report r squared for a bivariate linear correlation.

As explained in the earlier question, r = 0.74 which results in r squared of 55%.

The size of r is an excellent outcome but when r squared is taken into account (especially when 45% of the variance in the dependent variable remains unexplained), it sort of dilutes the message.

As pointed out in the answer to the earlier question, I do understand that it is not readily possible for a single factor to explain all the variation.

I think all statistical textbooks that I have consulted (unless I am consulting the wrong books!) state that r squared is a better way of understanding r (or the effect size).

I do understand though that r of at least 0.71 is needed to get r squared of 50%.

Questions

  1. Is reporting both r and r squared a good practice (in social science research)?
  2. When can I not report r squared?

I have asked Q2 in order to to avoid a situation like the above, where my non statistical target audience may focus more on 45% of the unexplained variance, rather than on the 55% of the explained variance.

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    $\begingroup$ Is it ever a good idea to report something when you have it? I realize there are different conventions for different sciences, but reporting $R^2$ is normal in economics. BTW, $R^2=.55$ is pretty good for a bivariate, non-time-series regression. Your biggest issue with a bivariate regression will be omitted-variable bias. $\endgroup$
    – jrhorn424
    Commented Nov 16, 2011 at 4:04

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You don't need to report both, either is fine.

Reporting R^2 does not "dilute" the meaning of R. That's like saying reporting your speed in kilometers per hour dilutes the meaning of speed in mile per hour.

In social science research, an R^2 of .45 is suspiciously HIGH.

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    $\begingroup$ Well, the sign of $r$ tells you the direction of the relationship, while $R^2$ does not. $\endgroup$
    – Macro
    Commented Nov 16, 2011 at 1:25
  • $\begingroup$ @macro Good point. $\endgroup$
    – Peter Flom
    Commented Nov 16, 2011 at 10:56
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I don't really feel like this question has an answer. It's sort of asking 'how do I pick a value for alpha in a hypothesis test?' I could explain to you what alpha is, but there's no rule or formula for picking an appropriate value. In terms of scientific research, you don't only report things when you want to, though.

Knowing that two variables have no relation is sometimes just as important as knowing that they do have a strong relationship. For example, if you designed an experiment, you may be interested in showing that two variables which are commonly assumed to be causal are in fact not related when viewed outside of an observational study.

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