Bob, I have a similar question to Sarah's and it may even be the same; I'm using orthogonal regression to determine the equivalence of two variables, both with errors. I want to use the S.E. of the slope to compare to the optimum slope of one (equivalence among variable responses). I contacted JMP (SAS institute) and they recommend the two-one-sided test (TOST) which I understand as simply increasing the alpha to 0.10. But this still gives a very large confidence interval providing a less than robust test. In some instances a slope of 2 is not significantly different than slope of 1. (!!??) In fact I have not found one instance in which the slopes differ. This seems like a universal type II error to me.
Can I use the standard test of homogeneity of slopes used in ANCOVA and compare to 1 (s.e. =0) or would that lead to a type I error? Thanks for your time, David David M Bryant Ph D University of New Hampshire Environmental Education Program Durham, NH 03824 [EMAIL PROTECTED] 978-356-1928 On Aug 16, 2006, at 9:39 AM, Anon. wrote: > 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
