I am running Pearson's correlation on an overall sample of 400 respondents.
When I isolate male and female responses, my sample becomes 220 male responses and 180 female responses.
If I further isolate male and female responses by (say) age groups, some sample sizes become as low as 35 responses (for example, for females over the age of 65).
My question: How good are these sample sizes for correlation analysis? (I am looking at the relationship between income levels and overseas travel.)
(I think this has something to do with margin of error but how does this apply to inferential analysis which is based on probability. I can understand its role in descriptive statistics such as results of a political poll).