I am quite new to Statistics, so please do not flame me for such a simple question.
I made a controlled experiment and successfully gathered the data. 41 persons participated. They made a questionnaire and a game. From both of them, they obtained a single, discrete score.
The situation is the following:
I split the 41 people in two groups A and B (those that obtained a score <= 0 in the questionnaire vs. those that obtained a positive score in the questionnaire). Actually, A is composed by just 6 of them but different splits may be possible under different reasoning. Let's just keep this one for now.
Therefore, I have two means for the game, X and Y, respectively. I would like to see if there are significant evidences that Y > X.
Which test should I use? I am really confused.
I continue to read around that if the sample size is > 30, I may use the T test anyway.
Then, there is the Mann–Whitney U test to be used for two samples if we can not assume Normal Distribution but should be applied for two samples of independent observation.
Any hints? Thank you very much.
Update: Ideally speaking, the population could also be categorized by the questionnaire score, I am trying to see if there is statistical evidence that people with a positive score also would have a higher game score