I've spent some time collecting participation data on a schools competition.
To sum it up:
Roughly speaking 1000 schools take part in the initiative every year. Only 10 schools become finalists.
The naked eye shows the % of Independent Schools increases significantly in the Finals.
The pattern is evident in the last 5 editions of the competition.
My intention is to prove independent schools are overrepresented in the finals. ... null hypothesis: both percentages are the same
What sort of statistical analysis shall I carry out to discard the null hypothesis?
Basically I want to compare percentages (% participant indep schools vs % finalist independent schools)...
is the analysis somehow compromised by the highly dissimilar sample sizes (n=1000 vs n=10)?
As I said the pattern is evident in all editions.. year after year... would this be an advantage to overcome the sample size problem?
Thanks in advance