# Statistical test to compare the mean of two samples

There's a competition with 20 categories, and each category has 3 winners. I have an array of the winner's performance of the next year (60 values), and other array with the average of the competitors of each category (of the next year also).

I wanted to compare them with the hypothesis: 'The winner of the competition will do above average next year'. It would be really useful if i could also do the comparison with only the two vectors of data (mean of winners/mean of competitors). I am interested only in verifying the hypothesis.

Is there any good Statistical test that could i use?

• How is "winner's performance" measured? Is this some sort of continuous measurements like time to complete a challenge, is binary (e.g. win/lose), or maybe even a count (number of challenges/test completed)? – StatsStudent Jan 10 at 14:31
• It's sort of continuous, like results (time) in distinct races. – Barry Allen Jan 10 at 14:34
• You have mentioned a hypothesis about the competition (i.e. all of the 20 categories combined), but have made reference to the 20 categories of the competition in the first paragraph. Is there then a single winner of the competition (or perhaps 3?) that you are interested in or are you really interested in the winner of the categories and comparing their means to their performance in those same categories the following year? If you are interested in the competition as a whole, how is the winner determined? By winning the most categories? – StatsStudent Jan 10 at 14:39
• @StatsStudent I am interested in the winner categories, and comparing their means with the mean of all the competitors for each category. I have a doubt with applying a t-test, should i run 20 t-tests? Or there is another way to do it? Thank you. – Barry Allen Jan 10 at 14:45
• OK. Please edit your question to make this clear. As it currently reads, you are mixing terminology that has created a confusing question, in my opinion. I do not see any major issues with running different $t$-tests now so long as you are interested in evaluating performance within each category separately. – StatsStudent Jan 10 at 14:49