Hi,
I am working on the home advantage.
And examining the difference of a player's performance between playing at home and away.
However, the sample size is different because the player played 5 home games and 8 away games. In this case, what kind of t-test is appropriate?
if all players are same at this 13 games paired t-test, but different players playing different 13 games independent t test must be perform. But your sample size ise too low, son non-parametric statistics better fit. Paired t test's non-parametric version is Wilcoxon test, independent t test's non-parametric version is Mann-Whitney U test.
A paired t-test works on before and after values for a certain phenomenon. In your case, you can use t test to compare between the two means (n1=5) and (n2=8).
For each player, you could calculate the mean (or median) of his home performances and the mean (or median) of his away performances. Check the distributions of these means (or medians) over all the available players. If this looks quite normal run the paired t-test, otherwise run the Sign test or the Wilcoxon signed ranks test. ( Sample size is not a criterium for decisding to use parametric vs. non-parametric tests; the normality of the distribution is more relevant)
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