# Parametric vs. non-parametric test.

#### med1234

##### Member
Dear all,

group 1: treatment A
group 2: treatment B

thickness of the skin was compared between group 1 (n=20) and group 2 (n=20)

I have used a non-parametric Mann-Whitney test resulting in a highly significant difference.

Now, the reviewer of my paper has rejected the submission with the following arguments:
"Why was the non-parametric Mann-Whitney test used? The data is numerical in nature. The sample size was reasonable. An unpaired two-tail t-test would seem the logical choice, unless there was a specific reason not to perform this test. Is the data normally distributed? This can be tested using a D'Agostino- Pearson normality test. Please present statistics as parametric (t-test) unless you can specifically explain why you are using a non-parametric test on this data. If it is because it does not obey normal distribution then present data qualifying this."

For me it is absolutely not clear why it should not be allowed to use a non-parametric statistic test. Even if data are normally distributed and with comparable variance, a non-parametric test would be allowed. If they are not normally distributed, a non-parametric test would also be the best. Can anyone explain to me if I am wrong and the reviewer is right - and if I really have to use an independent student t-test in such a situation.

Thank you a lot for your help
Chris

#### mogetons

##### New Member
I'm no expert, but from what I understand, non-parametric tests are less powerful that parametric tests are. Parametric tests should always be the first choice if data approximate the normal distribution and have reasonably similar variances. The t-test is apparently quite robust to non-normality, especially if you have equal sample sizes in the 2 groups.

Hope that helps a little.

#### Dason

##### Ambassador to the humans
I'm no expert, but from what I understand, non-parametric tests are less powerful that parametric tests are.
Only if the parametric assumptions are met. The parametric test can be robust (depending on the test) but if the assumptions are sufficiently broken then the nonparametric alternative will give superior results. I don't personally see what the reviewer has against nonparametric tests though...

#### med1234

##### Member
@Dason... yes, that's exactly what I do not understand. There might often be a reason against a PARAMETRIC test (e.g. no normal distribution), however I can not understand what should be the problem when using a non-parametric test in my case --- as even with the non-parametric test the result is highly significant... is anyone here that might further help in this issue... either arguing against or in favor of the non-parametric test in my situation? thank you a lot

#### med1234

##### Member
yes - non-parametric test might be less powerful, but in my case I have a highly significant difference even with the non-parametric test, therefore I do not understand why I should not use it. So I do not really depend on normal distribution etc.

#### CB

##### Super Moderator
Now, the reviewer of my paper has rejected the submission with the following arguments:
"Why was the non-parametric Mann-Whitney test used? The data is numerical in nature. The sample size was reasonable. An unpaired two-tail t-test would seem the logical choice, unless there was a specific reason not to perform this test. Is the data normally distributed? This can be tested using a D'Agostino- Pearson normality test. Please present statistics as parametric (t-test) unless you can specifically explain why you are using a non-parametric test on this data. If it is because it does not obey normal distribution then present data qualifying this."
What's interesting here is that the reviewer seems to be coming at this with the position that you should use a parametric test unless there is a compelling reason for not doing so. However, they haven't articulated a reason for why one should take this position. Maybe they do have a specific reason - e.g. perhaps because they see switching to a rank-based test as abandoning some information about the data points, or because they might feel that the Mann-Whitney test has a less clear interpretation than a t-test. But it's hard to tell what their reasoning is, because they haven't made any justification for their position. Unfortunately, it's fairly common for people to take this position.

I think it's reasonable, though, to expect you to justify your choice of analysis in the article, regardless of which test was used. So perhaps this is something that needs to be discussed more explicitly in the article. Correspondingly, it should also be ok for you to question why the reviewer is taking the position they have without any justification.