[While approving this message for the list, I have added a response. --Will]
I have a query regarding repeated measures data. I have a baseline measurement, and 3 post intervention measurements - and due to the large variability of the data I am collecting, I have found it much more meaningful to normalise the data. So baseline is 100%, and all post-intervention measurements are normalised to that i.e. an increase of 10% would be represented as 110%, or a decrease of 10% would be 90%. [That's not "normalizing" in the usual sense. But what you are appear to be saying is that the post-test values, as a percent of the pre-test, look more like a normal distribution. Or it could be that the effect of the intervention on each subject looks about the same for each subject, if you represent the effect as a percent of baseline rather than as an absolute value. Whatever, if you think percents rather than absolutes are involved, the first thing to try is log transformation. You transform pre and post values, and analyze those. You derive the percent effect from the analysis of the log-transformed variable. I explain how at newstats.org.] Whilst this gives a much clearer picture to myself and the reader as to the changes that have occurred over time, it has given me a statistical query. Is there anyway I can analyse the normalised data statistically? If I did a repeated measures then all the baseline data would be 100%, and therefore have no standard deviation at all - would this affect the analysis? I have analysed the raw data with a repeated measures, but because there is so much variation in the data, any changes are 'drowned out' where-as if I normalise each individual to their baseline I can see quite clear changes occurring over time. [You use the usual statistical modeling--ANOVA and such--on the log-transformed variable. You should check that the transformation is appropriate by viewing a plot of residuals vs predicteds. You can also use the t statistic on the percent change scores you have calculated without using logs. For modest percent changes (~10%) it will give the same answer. For larger percent changes, the answer from log transformation is probably better, but it depends on the uniformity of the residuals of the log variable compared with the uniformity of the percent changes of the raw variable. This is a subtle point that you shouldn't worry about, because no-one has ever compared log with percent transformation. Just use logs. Nature is usually logarithmic. Note that, as I state at my stats site, the change in the mean (or in the value of any other kind of effect derived from log or any other transformation, including your percent approach) differs from the value derived directly from the raw numbers. Which approach gives the "correct" value? Answer: the approach that gives the best uniformity of the residuals, because uniformity of residuals means that, apart from random error that is of the same magnitude for every subject, the mean applies to every subject. (There can still be consistent individual responses...) And as I stated in a posting some months ago, the value for an effect derived from a transformed variable that gives uniformity of residuals and therefore a symmetrical distribution of residuals is a kind of parametric or superduper median, although the only responder did not seem to understand or appreciate this idea. See message #2443 http://sports.groups.yahoo.com/group/sportscience/message/2443 and the response #2451.] Any help or advice is always greatly appreciated. Emma Hawkes PhD Research Student Brunel University Uxbridge Middlesex UB8 3PH UK ------------------------ Yahoo! Groups Sponsor --------------------~--> Help save the life of a child. Support St. Jude Children's Research Hospital's 'Thanks & Giving.' http://us.click.yahoo.com/6iY7fA/5WnJAA/Y3ZIAA/2_TolB/TM --------------------------------------------------------------------~-> Post messages to [EMAIL PROTECTED] To (un)subscribe, send any message to sportscience-(un)[EMAIL PROTECTED] View all messages at http://groups.yahoo.com/group/sportscience/. Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/sportscience/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
