We're all guilty. We run those regressions and just hope to see those little stars, those p values less than .05. Often students come to my office excited to show stars without even peaking at the coefficient estimates. Drafts of papers are written that say "and the estimate is significant" without even mentioning what the estimate is, never mind trying to figure out whether it is big or small or even reasonable.
But what is the best way to interpret our estimated coefficients? How do we put those numbers in perspective, especially when our variable of interest is an index or test score or something else that readers may not have personal experience with? One possibility is to say something like, "the effect size is about half a standard deviation.." What does this actually mean? My old friend, Lionel Page, comes to the rescue with some handy dandy pictures. Even with effect sizes of 2 standard deviations, there is still quite a bit of overlap in the two distributions! By all means, compare means...but please, stay humble!
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