P.Mean: Example of power calculation for a repeated measures design (created 2008-10-11).

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I was asked how to calculate power for an interaction term in a repeated measures design. There were two groups (treatment and control), and subjects in each group were measured at four time points. The interaction involving the third time point was considered most critical.

Let's think about what an interaction means. Each group is going to have a time trend across the four time points. What is that trend likely to look like? I don't know what this person had in mind, but let's suppose that he said that there is an increasing trend in both groups, but he expected an attenuation of this trend in the treatment group.

It's impossible to list all the possible scenarios where there are increasing trends with attenuation of the trend in the treatment group. Instead find one, two, or three plausible scenarios. The general assumption (and one that is usually reasonably justified in my experience) is that if a research study has good power for one scenario then the study is presumed to have comparable power for comparable scenarios.

The outcome variable in this study is the Oswald Disability Index which ranges from 0 to 100. I do not know the standard deviation for this outcome measure, but a quick review using PubMed showed hundreds of articles that use this scale. Here is a table from one of these studies:

www.painphysicianjournal.com/2008/august/2008;11;491-504.pdf

You need to read carefully elsewhere to discover that the number reported after the +/- is a standard deviation rather than a standard error. Tables 1 and 2 include the words "Mean +/- SD" so it is safe to assume that table 4 uses that same format, even though it is not explicitly stated.

The problem with this table is that the standard deviation is a total standard deviation that incorporates both between and within subject variation. The interaction test requires knowledge of both the subject variation. It would be worthwhile to search through some of the other publications at this point.

Another publication states:

The mean difference in change in ODI scores of those participants in the FairMed and those in TENS groups was 0.4; this difference in change was not significant (p = 0.85). www.biomedcentral.com/1471-2474/9/97

A third publication has a graph

www.springerlink.com/content/38231705703ttt53/fulltext.pdf

and

www.biomedcentral.com/content/pdf/1471-2474-7-82.pdf

Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. This page was written by Steve Simon and was last modified on 2010-04-01. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at .