I am going back and forth on which tests to do.
I have two paired variables, that are both positive integers (0,1,2,3…etc). $n = 559$. The variables represent the error resulting from two different methods. I want to know if I get the smallest error using method 1. I turned to the paired t-test, which requires normality of difference between the two variables. But is it even possible to use this when the data is discrete? The histogram (with normal distribution plotted on top) and a qqplot can be seen in attached figure. As an alternative I have looked in to wilcoxon signed rank test – would this be more suitable?
I appoligize in advance for any wrong statements – I am not a statistician.
Best Answer
Just to expand on why the t-test is working: this is a result of the Central Limit Theorem, which tells us that the sample mean has a Normal distribution as $n$ grows. Your data is clearly non-normal, taking discrete values only, but the sample mean will be fairly Normally distributed on account of your large sample size.
If your sample size was much smaller then the Wilcoxon signed-rank test would be more suitable, avoiding the Normal assumption.