# Appropriate tests on discrete and paired data

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.

• Your data looks fine for a paired t-test. You can also apply a Wilcoxon test but my guess is that you'll get the same result. – Digio Sep 13 '17 at 19:37
• Thank you for the answer Digio :) I have done both tests and got the same result. It does not matter that my variables can only take discrete values (0,1,2,3....... etc)? – SupAnne Sep 13 '17 at 20:09
• As long as you keep them in your software as type numeric, they're seen as integer numbers (not discrete values), which is fine. Just make sure you don't convert them to factor levels. – Digio Sep 14 '17 at 8:55
• What exactly are you trying to do in real world terms (not statistical ones)? Can you describe your problem? I suspect you might be going about this incorrectly. For example, if you are you interested in choosing the best predictor between method A and method B? if that's the case, why not simply build a model on a training data set with method A and then separate with method B, and then select the model that has the smallest error when applied to a validation data set? – StatsStudent Feb 19 '19 at 1:30

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.