# What is the right hypothesis test for this problem?

I would like to discuss and analyze what is the best hypothesis test for this problem:

We have data with the distance that each football player of each team runs in a match. Now we want to find two teams with the most similar pattern (by comparing any combination of teams).

I agree the word "similar" is not clear in above statement. My interpretation is to find a hypothesis test that helps to find the same underlying distribution.

The to formalize the question: Suppose x and y are vectors representing distance that players in each team run. Also, we suppose the position of players from goalkeeper to forward is sorted in the list. To prevent confusion lets just suppose there are only 11 players and we are not considering substitute players.

Null hypothesis(H0): x and y doesn't have the same distribution

Alternative hypothesis(Ha): x and y have the same distribution

Then we need to find a test so that the returned p-value is less than a significance level (alpha) (for example alpha= 0.05) so that we can have against evidence against the null hypothesis and (Ha) can be accepted.

I guess the data is paired(dependent) data because we are comparing two group with the same structure. however I am not sure about it.

Link to previous related question: Interpretation of p-value in Mann-Whitney rank test

• Your question is about finding the "best team", which implies (I think) that there are many teams being considered. But your proposed test only compares two teams. Please clarify. Jan 31, 2017 at 14:23
• you are right. what I mean was to compare any pairs of teams and find the best combination. I will update the question Jan 31, 2017 at 15:18