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.