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  • how can a correlation coefficient of .40 be a "medium" effect size when r2 shows that the variables only have 16% common variance? Seems like the 16% suggests a small effect size. Jim
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  • $\begingroup$ (correlation coefficient)$^2$ = r$^2$. $\endgroup$ – user158565 Feb 14 '19 at 18:20
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There is no absolute way to describe the strength of an effect - it is all relative. When you hear someone refer to a "small," "medium," or "large" effect size, they are referring to what effect sizes are commonly seen within their field of study and/or what is to be expected from the phenomena being studied.

When you hear things like "r = 0.1 is weak", "r = 0.3 is medium" or "r = 0.5 is strong" it generally refers to guidelines for the social sciences. This is because humans tend to be very complex compared to the methods used to study them (i.e. data from humans is noisy). So effect sizes tend to be smaller. However, we would expect higher effect sizes in a field such as industrial design, where the phenomena being studied can be controlled to a much greater extent.

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Yes and no. Effect size meanings depend on what they measure. For example, if you measure an effect of a drug on weight loss, you will end up with some distribution describing the weight changes in your experiment group. In this case, the (mean standartized) effect size will be the ratio of that distributions mean and standart deviation. It will be a real number - not nescesarily between 0 and 1. It will also be a practical number meaning the actual effect on weight distribution shift in its standard deviations. In the case of correlating things, you can use the r2 for comparing different model "fit" to the data. Also note that r2=1 means that the datapoints are ideally represented by the model. In practical cases very high r2 is an indication of overfitting. Real data is always noisy.

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