# Whether to use nonparametric tests to compare two groups when sample size is large but assumptions are violated

I have a data set that has 600 observations divided in two groups. I am going to compare the central tendencies (e.g., the means) of these two groups. However, there are violations of classical assumptions present, such as normality and equality of variances.

• Can I use a parametric approach (specifically, the t-test), since the sample sizes are large (based on the Central Limit theorem), or do I have to use a non-parametric approach?
• If I should use a non-parametric approach, which test (Mann-Whitney, Median or Kolmogorov-Smirnov) is most appropriate?
• May 16, 2012 at 4:22
• Whether or not the central limit theorem has effectively "kicked in" by a given sample size depends on the distribution of the data. In most cases that come up, $n = 300$ in each group would be enough. It's mainly unusual examples that "break" the CLT for finite samples. For example, if your data were all Bernoulli trials with success probability $p = 10^{-9}$, your sample of $n=300$ outcomes would almost certainly be all 0s, so the sample means are, of course, not approximately normal - a much larger sample size would be required. May 16, 2012 at 12:35