Means instead of medians for non-parametric statistical tests?

MATLAB's Wilcoxon signed-rank test and rank sum test both test for medians of data. However, I'm only interested in the mean values of my data and want to perform a non-parametric test for these means. Is there a way to work around this?

I know the good old t-test tests for means, but my data doesn't follow a normal distribution.

Answer 1

[Star Strider]

If your data do not follow a parametric distribution, or you don’t know the distribution, use a nonparametric test, and accept the test on the medians.

If you are using a paired design (for instance using the same population to observe the effect before and after a particular intervention), use the signed-rank test. If a non-paired design (intervention on one group of two), use the rank-sum test.

If your data do not meet the assumptions of a particular test, such as requiring in part that they be normally-distributed, you cannot use a t-test.

[Juha]

Thanks for clarification.

I must use the signed-rank test, even though the p-values I get from it don't make any sense with the bar graph of means (+/- SEM) I have. One pair of data has a large difference in means but is not statistically significant, while another has virtually no difference in means but gets a p-value less than 0.01...

[Star Strider]

My pleasure.

You could certainly get those results with a highly-skewed distribution. The mean is sensitive to extreme values, whereas the median is not. The median and the mean in such data would likely be quite different. A boxplot of your data would likely be informative.

[Juha]

I found out the source of my problems. My data has values between -1 ... +1. Matlab's signrank function seems to have problems with negative ranks. I solved the problem by scaling my values to 0...+1. Got the right p-values now.

[Star Strider]

Interesting. Linear scaling should not affect the validity of your data or statistics.