# How to assess (properly) a difference between two samples of integer responses

Consider the following scenario: A group of students (N=85) is given a test to assess their knowledge, the test contains a single question with four possible responses: 0,1,2,3. Students have to make a test twice: before and after a class, to check whether the class had any effect on their knowledge.

Question: which statistical test is the most appropriate in this setting? (paired t-test, Wilcoxon, permutation test, chi-square with several categories, etc)

What bothers me is the fact, that the integer numbers are not real (R) numbers, but rather 'categorical', so application of the t-test etc doesn't seem to me the best approach (although the sample size is relatively large, which in principle, does not contradict the t-test assumptions)

• So, you have one Q, with four possible answer alternatives, of which exactly one is correct? And, you give the test twice, before/after lecture? Maybe you could reduce this to a 2x2 contingency table? Or, you could have response variable correct/incorrect, then a logistic regression with a random intercept , that is, one intercept by student? Or it is important to model the specific wrong answers? – kjetil b halvorsen Feb 28 '17 at 15:24
• @kjetilbhalvorsen, there is no 'correct' or 'incorrect' answers, just ranking (0,1,2,3). for example a possible test might be as: 'Are you happy with your knowledge?', where 0 - not happy, and 3 is very happy. For example, before the test ,students did not know anything about economics (the average test score should be close to zero) and after the test they know much more (the average score should be close to 3). – Arnold Klein Feb 28 '17 at 15:28
• Thanks, then you should edit the post to make that clear! And for that reformulation, maybe an ordinal logistic regression? Maybe with a random intercept for each student? Then this may be relevant: stats.stackexchange.com/questions/238581/… I will think about simpler approaches! – kjetil b halvorsen Feb 28 '17 at 15:33