# 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. – Harvey Motulsky Jan 31 '17 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 – Woeitg Jan 31 '17 at 15:18

## 1 Answer

"Now we want to find two teams with the most similar pattern" doesn't seem to be a hypothesis testing problem.

Once you define what "most similar" among pairs of patterns for teams is (or conversely, what most dissimilar is), it seems to be a matter of calculation to find the most (or least, if you measure dissimilarity) extreme case.

[If you had one pair for comparison, you might do an equivalence test (rather than a more typical hypothesis test), but you might end up with several that are equivalent, or none; it doesn't pick a "most".]

• Thanks for the answer. Let's say the most similar measure is mean. Can you give me more info on equivalence test? I suppose it is a group of tests. I want to test it in python – Woeitg Feb 1 '17 at 8:13
• You can find the two teams with the means that are closest by direct calculation -- that ("find the most similar") is not really a statistical problem but an optimization question. You may want to identify a slightly different question – Glen_b Feb 2 '17 at 7:06
• @Woeitg If you are seeking basic information on equivalence testing then aside from posts on site, there are a number of papers. This one might be of some use. – Glen_b Feb 3 '17 at 3:50