I have a simple contingency table with two nominal variables. Let's say Age and Gender. The software that I'm using reports the relationship between the two variables using Pearson's Chi-Square Test of Independence, to which I understand.
But when I select only two cells in the table and try to do a test for that, the software reports it still uses Pearson's Chi-Square Test of Independence, but use it to test the difference in the population (see below).
Q: Why does the software use the same Chi-Square test to test the difference in the population for the two cells I select. Shouldn't that be a t-test? Shouldn't that the chi-square be used to test the relationship for the two variables,
Q: Statistically, what's the interpretation if I try to do a hypothesis testing on only two cells in a table?
Total sample Unweighted base n = 327 Pearson's Chi-Square Test of Independence Chi-Square = 0.023 Degrees of Freedom = 1 n = 327 Effective Sample Size = 327 Agresti, Alan (1990): Categorical Data Analysis, John Wiley & Sons: New York, pp 24-25, 47-48. p = 0.88 Not significant Null hypothesis: There is no difference in the population between the proportion of '18 to 24' of people in 'Male' than 'Female'. At the 0.05 level of significance, the null hypothesis is not rejected.