I want to compare two distributions, to see if they are significantly different. They represent task time completions (so they range from 1 to around 1000 seconds) in two different months. They are not normally distributed. I want to see if their central tendencies are significantly different (at a first glance the mode, mean and median between the two months seem very close, just 3-4 seconds difference), but also to see if their shapes are similar (again, at a first glance, they look similar). I am currently carrying this analysis with SPSS 20. I have the Mann-Whitney test for testing central tendencies and the Kolmogorov-Smirnov test for the shape of the distribution, (although I have read that the K-S test is an overall comparison test for the distributions).
Also, in the first month I have 300,000 observations and in the second month 122,000 observations. So, a lot of data ... but disproportionate. Is this an impediment to running these tests, the fact that the sample sizes are not equal? I ran both Mann-Whitney and K-S and they both seem to reject the null. How much should I trust the results given my sample sizes? Do you suggest any alternative tests? Thanks