You are more likely to see significant results for large samples. This is one desirable feature of this test statistic. See the example below. The differences in the small sample are not even remotely close to being statistically significant. We observe the same differences in both samples, but we are more confident in the results of the large sample and, in fact, we must conclude that gender and party id may be unrelated if we only have the small sample to analyze A Note on Theory and Data.
Correlation is empirical.
We may observe a statistically significant relationship between income and party identification. Causality is theoretical. It is not difficult to come up with a plausible and internally consistent story about the link between affluence and identification with the Republican party. As incomes increase, individuals face a higher and higher tax burden, so they become more and more averse to taxes. Republican candidates consistently advocate lower taxes, so these high income individuals prefer Republican candidates.