# ttest or wilcoxon

for a user study I want to compare some tasks. Each tasks has 2 conditions on a intervall scale. From each task I want to test the the conditions with:

• a t-test if both samples are on a normal distributions
• a wilcoxon, if both samples are not on a normal distribution

but what test I can choose, if one sample of a task is on normal distribution and the other is not?

I've read something about, that I can run samples from a normal distribution with a wilcoxon test, too. Are there some benefit of the t-test for normal distribution samples? Why should I not test all my samples with the wilcoxon?

• @Glen_b, Just a heads up, I think I know what your asking, but you might want to spell check this comment. – k6adams Apr 25 '15 at 14:48
• I'll try that again: On what basis can you know that one sample is from a normal distribution? – Glen_b -Reinstate Monica Apr 25 '15 at 18:26

In general, because the Wilcoxon does not assume normality, it is a more conservative estimate. For example, say you conducted a t-test on normally distributed data, and the p-value of that test was marginally significant, $\approx .05$. Chances are if you were to conduct that same test using a Wilcoxon, then the p-value is likely to be $> .05$. You may concluded that there is no evidence to conclude that the two populations are different when in fact there is evidence.