# Possible new statistical test

Imagine a scenario where someone walks into a room with ten adults. Five of the people are in their twenties and are children of the other five people (who are in their fifties). The person who just came in is tasked with determining based on family resemblance who goes with who.

I'm trying to either find or develop a statistical test that can determine a p-value for getting a certain percentage of guesses correct. But I'm sure there's a test already out there. I just don't know what it would be called or how to go about searching for it.

I'm aware that technically, a chi-squared test can be used. A lot of nCr and nPr calculations would have to be made to determine the expected frequencies of getting matches right. But I would think that if this test has been developed, someone would have made a test to address this exact situation.

Again I'm not sure how you would even go about describing this test so I'm not sure what I would search for. Would we call this a "non-independent Bernoulli trial of matches without replacement"?

Simply put, my question is "is there a hypothesis test that was custom made to address this kind of situation. And what is that test called (if it exists)?"

Regards

• This sounds like a classic counting problem. Jul 6, 2021 at 2:15
• Are these pairs of one parent to one child, or can someone have multiple parents or children present? Jul 6, 2021 at 11:07
• Ultimately I was going to look at both of those scenarios. Jul 6, 2021 at 13:25

• What is the benefit of doing a permutation test, especially if we already know the probability distribution of guessing $x$ correct pairs? In my opinion, there is no parameter to estimate hence no hypothesis to test. Its simply a matter of computing the $\operatorname{Pr}(k \leq X)$ Jul 6, 2021 at 3:07