In a chi-square test, what do expected frequencies refer to?

Expected frequencies in a chi-square test refer to the frequencies that would be expected if the null hypothesis is true. This entails calculating what the distribution of frequencies would look like based on the assumption that there is no association between the categorical variables being tested. For instance, if you are testing the relationship between two variables, the expected frequencies help to determine how many occurrences of each category combination you would anticipate under the null hypothesis, assuming the variables are independent.

This contrasts with the actual frequencies observed in the data, which represent real counts from the sample, as stated in one of the other choices. The expected frequencies are crucial because they serve as a benchmark against which the observed frequencies are compared to evaluate how well the observed data aligns with what we would expect under the null hypothesis. If the observed frequencies deviate significantly from the expected frequencies, this suggests that the null hypothesis may not hold true, prompting further investigation into the relationship between the variables.