Mean or median

[Melk]

I am comparing 2 groups in some baseline measures. One of the groups is rather small (n=6) while the other is moderate at n=20. Should I use the mean or median in my table and my group comparisons? My concern is, with a sample size of 6 in 1 group, the wilcoxon test just seems less powerful than a t-test.

[PaigeMiller]

To tell you the truth, the decision on whether or not to use a mean or a median depends on what you intend to do with the statistic (which you haven't told us) and also whether or not the distribution of the data is skewed or not.

If the distribution is not skewed, and is relatively symmetric, the mean and the median ought to give very similar answers.

Regarding the Wilcoxon test, I believe it is ALWAYS less powerful than the t-test ... but I guess I haven't actually seen that proved either. Maybe Wilcoxon is less powerful for relatively symmetric distributions, and more powerful for very skewed distribtuions? I'm guessing...

But the answer depends on the symmetry or skewness of your distribution, and not really on the sample size.

[Melk]

I will be comparing baseline values between the 2 groups using a 2 sample t test or mann whitney u as appropriate.

The issue for me here is that with N=6, it is difficult to assess symmetry and skewnesss, so I usually resport to non-parametric methods, but I wondered if anyone else had other suggesstions.

[PaigeMiller]

I probably could have written a clearer message. What I should have said is that you want to judge the symmetry or skewness of the populations; it really doesn't matter what the symmetry or skewness of the sample is.

Now, it may be that you don't have any idea about the population, but for some populations you might have a good idea that the population is skewed, or not.