# Is it wrong to do a Linear Regression here?

I'm an undergrad doing an internship in a lab. My statistics background is very poor. I pretty much know what analysis to do on my experiments only because I read this, and I have statistical software that I command 'do a t-test pls'.

I'm studying memory, I measure the escape response of the animal, if the escape response is significantly lower than in testing, I can say there is memory. Here is what I can do with my data.

a) On most of the experiments homoscedasticity assumption is violated, so I do non-parametric t-student if there are two groups, or non-parametric anova is >3 groups. Let's say there are two groups, Control and Trained, I find that the Trained group has a significantly lower escape response (comparing the mean of CT vs the mean of TR), the experiment went how it was supposed to do and everyone is happy.

b) Same situation but, even though I can see a tendency, the difference is not statically significant (what happens most of the time). What I was told to is to relativize the data. How I do that? For each animal I take my Testing observation and I divide it by the maximum observation I have of THAT animal (the maximum can be observed in either training or testing, I expect the maximum of my control groups to be on the testing session, and the maximum of my trained group on the training session). So, the relativized score is TS/Max. I then do the anova/t-student and the tendency I saw on the raw scores is now statically significant.

Now, there is some argue in the lab about doing that. There is no doubt that from a biological perspective there is no problem in doing that. But on the statistics front, some people say you shouldn't, some people say it's fine (most people of the lab are biologists, but we consulted with statisticians)

What I'm asking Can I do a linear regression, where instead of having one observation for each animal (the testing raw score) I add a (moderator? mediator?) variable, the maximum it got on either training/testing?

Thanks in advance, I'll happily respond if anything is not clear (sorry, english is not my mother tongue) and I can provide a data set if needed.

• I don't know what you mean by "non-parametric t-student" there. If you can't assume equal variances, one would normally use something like a Welch-Satterthwaite t-test, but that is in no sense non-parametric (or at least in no sense that I can think of). Please clarify your question. – Glen_b Apr 5 '16 at 0:13
• I think I didn't express myself right. I didn't remember the name of the analysis, but I checked it and I do a 'Mann–Whitney U test', and, as far as my understanding go, that's the 'non parametric version of the student's t-test' (if your data violates homoscedasticity / normality you can't do the parametric tests like anova or t-test, so you have to do the 'non parametric' versions of those) – Nick Starker Apr 5 '16 at 0:26
• You could regard it as a nonparametric version of the t-test (though it's not the only "nonparametric version of the t-test", and it's only suitable as a comparison of means under additional assumptions, which won't necessarily be consistent with differing variances); we can't reliably infer that you mean Mann-Whitney by that phrase. If I had to interpret the phrase "non-parametric t-student" I'd have guessed you probably meant something else. As I already said above, not assuming equal variances under the null would lead me to do a different test --- but not a nonparametric one. – Glen_b Apr 5 '16 at 1:35
• Ok, thanks, I get it. I don't want to seem like an asshole to someone that is trying you help me, but what do you think about the thing I asked? Doing a Multiple regression analysis introducing the 'maximum' as a variable? Does it make any sense? Sorry if I sound rude or something – Nick Starker Apr 5 '16 at 1:38
• I'll try to come back later and convert my earlier comments to a response to (a) and write something as a response to (b) - which will be along the lines that doing a different test if the first one fails to reject is flat out significance-hunting. Construct the best test you can make for your hypothesis of interest (which might conceivably involve some scaling of the data to make it comparable though there are other choices there) and test that; if your best available test doesn't reject, that's the end of it, you don't get to keep playing with your data until something significant pops out – Glen_b Apr 5 '16 at 2:03