Sarah Gilman wrote: > Is it possible to calculate the standard deviation of the slope of a > regression line and does anyone know how? My best guess after > reading several stats books is that the standard deviation and the > standard error of the slope are different names for the same thing. > Technically, the standard error is the standard deviation of the sampling distribution of a statistic, so it is the same as the standard deviation. So, you're right.
> The context of this question is a manuscript comparing the > usefulness of regression to estimate the slope of a relationship > under different environmental conditions. A reviewer suggested > presenting the standard deviation of the slope rather than the > standard error to compare the precision of the regression under > different conditions. For unrelated reasons, the sample sizes used > in the compared regressions vary from 10 to 200. The reviewer > argues that the sample size differences are influencing the standard > error values, and so the standard deviation (which according to the > reviewer doesn't incorporate the sample size) would be a more robust > comparison of the precision of the slope estimate among these > different regressions. > Well of course the sample sizes differences are influencing the standard error values! And so they should: if you have a larger sample size, then the estimates are more accurate. Why would one want anything other than this to be the case? In some cases, standard errors are calculated by dividing a standard deviation by sqrt(n), but these are only special cases. It may be that the reviewer can provide further enlightenment, but from what you've written, I'm not convinced that they have the right idea. Bob -- Bob O'Hara Dept. of Mathematics and Statistics P.O. Box 68 (Gustaf Hllstrmin katu 2b) FIN-00014 University of Helsinki Finland Telephone: +358-9-191 51479 Mobile: +358 50 599 0540 Fax: +358-9-191 51400 WWW: http://www.RNI.Helsinki.FI/~boh/ Journal of Negative Results - EEB: http://www.jnr-eeb.org
