Hi Daniel

I am not sure why the test being non-parametric is relevant to the direction of testing. Generally, 2-tailed tests are used for all clinical trials, but if you have a very strong argument for a 1-tailed test, then it is acceptable.

Adrian

Yes, you definately need a 1-tailed test. Such a 1-tailed test is necessary if you have a directional alternative hypothesis (i.e. that A is larger than B). Therefore, I would have thought, 1-tailed tests are essential in clinical trials because you are always interested in whether one therapy is better than another not in just that they are different (at least, my medical collegues tell me they're interested in finding which therapy is better !).

There are two things in your question that trouble me, however. One is talking about a 'dependent' variable. The second that is saying that group B is expected to have a frequency approaching zero. In a pair-wise test neither variable is dependent or independent. And how do you have frequencies approaching zero ? Does that mean that B cannot, even in theory, fall below zero ?

Andrew

Thank you for your replies. My question is primarily because I'm thinking about trying newer and possibly more appropriate statistical techniques in my next project.

We have two independent groups separated on a biological variable we expect may increase the frequency of occurrence of a clinical endpoint. We want to test the difference in frequency between these groups, and the frequency cannot possibly be below zero for either group. It's also highly unlikely to be normally distributed. Also, with one group expected to be at or near zero, it seems likely that there will be a big difference in variance between groups.

Hallo Daniel,

We have to be clear about what Mann-Whitney does. It tests whether two samples have the same median. The two samples could have the same median but different means, or different shapes.

And if you're testing frequencies perhaps a contingency table would be more appropriate ?

I really need more information about your experiments and the kind of data you expect to get.

Yes, if you aim to analyze the frequencies of the outcome, a logistic model (logistic regression) [that's the tool to analyze contingency tables] should be thought of.

@Andrish, just to mention: the MW-test is *not* about testing medians. It is a rank sum test, it tests the rank distributions. This is generally hard to understand what this actually means. The test is particularily sensitive to stochastic shifts (but this is just one aspect). *Only* in the case of identical shapes for the two samples is this identical to "tesing the medians". I can give you samples with identical medians where the MW-test gives a very tiny p-value.

If you're concerned about using a non-parametric analysis (because of highly variable data), you can do a log-transformation (or some other transformation), followed by some appropriate parametric analysis. Either way, if you are predicting a unidirectional outcome, based upon your own or others' data, it's legitimate to use a 1-tailed test. However, your statement that "the null is that they are equal" is not correct. You can "prove" significant differences statistically but not that they are equal, as I recall from my understanding from long ago. You may also consider using a test based upon the variances, instead of upon the means or medians, etc.

Don't worry about undertaking a non-parametric test. Even if the data were Normally distributed, the most power you can lose is ~15%. In my opinion, non-parametric tests are greatly under-used.

I'm thinking the Mann-Whitney U would be the appropriate test, but I'll read further into contingency tables and logistic models before proposing anything.

Thank you for all the great feedback.