>Date: Tue, 21 Mar 2006 09:48:44 -0800 >From: Chris Caudill <[EMAIL PROTECTED]> >Subject: transforms and CIs > >Hello all, > >Here's a question that I feel like I should know the answer to... > >I've conducted an ANOVA in sas on a large data set using log(e) >transformed data. I'd like to plot means and 95% CI's using the sas output. > >Is it kosher to simply back-transform the CI's (I have a nagging >feeling that it isn't). Thanks in advance. > >Chris Caudill > >Christopher C. Caudill >Department of Fish and Wildlife Resources >College of Natural Resources >University of Idaho >Moscow, ID 83844-1136 >208-885-7614 (voice) >208-885-9080 (fax) > >http://www.cnr.uidaho.edu/UIFERL/Christopher_C._Caudill.htm > >NOTE NEW EMAIL: >[EMAIL PROTECTED] >
It's OK to back-transform the confidence *limits*, not the confidence *intervals*. Remember, you log-transformed the data because it was non-normal; it was log-normal, in fact. The 95% confidence interval tells you that you are 95% sure the true mean lies within that interval. With a symmetric, normal distribution, this interval will be symmetric around the mean. Because a log-normal distribution is not symmetric (at least in untransformed, "real" space), the interval in that space won't be, either. So what you need to do is figure out what the 95% upper and lower confidence limits are in log space, then transform those values back to real space. Your confidence intervals won't be symmetric, nor should they be. -- Richard L. Boyce Department of Biological Sciences Northern Kentucky University Nunn Drive Highland Heights, KY 41099 USA 859-572-1407 (tel) 859-572-5639 (fax) [EMAIL PROTECTED] http://www.nku.edu/~boycer/
