On 8/16/06, David Bryant <[EMAIL PROTECTED]> wrote: > > 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. =3D0) or would that lead to a type I error?
I would just look at the CI for your slope estimate and see if it included 1. 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 H=84llstr"min 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 >
