statistics - unequal sample sizes


I have a long held assumption that when comparing two groups with very unequal sample sizes, it's better to use non parametric tests (Mann-Whitney U). So today I was merrily doing that, when I though, "why is this? and where did I get this assumption from?". So I've looked in a couple of books and can't find anything reccomending non-parametric tests for this situation. Has anyone got any pointers? Worst case scenario I need to compare n=5 to n=32.


and I get exactly the same answer whether I use t-test or Mann-Whitney.


Hi, well if you get the same results then it doesn't matter, but I would go for the non-parametric test with such small numbers.


As far as I understand (someone please tell me if I am wrong!), you use a t-test if your data has a normal distribution (e.g. bell shaped curve with histogram or nice even spread on a boxplot) and equal variance. If your data does not have normal distribution/ equal variance, you use a non-parametric test such as mann-whitney. If you have two groups to compare, they both have to have normal distribution/equal variance. If you have three or more groups (e.g. ANOVA situation) the same assumption or normality/equal variance holds. So it isn't having five samples per se that is the problem, the problem is that if you only have 5 samples, your data probably isn't normally distributed. Even if you had 2000 samples if they aren't normally distributed, a non-parametric test is much more robust. Hope that makes sense. Good luck!


Kbara, any particular reason you'd go with non-parametric?

Thanks for other response. That's what all the books say, but I'm sure I had a reason to think non parametric was better when sample size was very smll and unequal, I just can't remember where I got that from. The five do conform to normality using testing...... but it could be those tests don't have the power to pick up deviations form normalitity with a small sample....


I think its possible. there other tests you have to report like tests for levenes test of homogeneity and Welch test of equality of means. so once u report the results u can go ahead with the t test