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Assuming normal distribution, one SD is equivalent to an effect size of 1.0, which is associated with a gain of 34 percentage points from the average. From a simple regression model, if past achievement, a score from E to A grade, predicted a change of one SD in current achievement, a standardized score (mean of 0), can I infer that an increase of one letter grade in past achievement (e.g., C to B) can result in a 34 percentage gain in current achievement? Or would it be more correct to say "can explain about 34 percentage of the variance"?

Any comments appreciated. Thanks!

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The change in the normal CDF moving from 0 to 1 is .34, but the change associated with moving from 1 to 2 is about .136, so there is no constant change in percentage points associated with a change in zs of 1. Other than this, I don't quite follow your question. – gung Jan 17 at 5:36
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It doesn't work the way you seem to think. You're confusing a bunch of different things together. – Glen_b Jan 17 at 6:18

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