What statistical method directly utilizes expected frequencies for hypothesis testing?

The Chi Square test is the statistical method that directly utilizes expected frequencies for hypothesis testing. This test is commonly used to examine the association between categorical variables, where it compares the observed frequencies in a contingency table with the expected frequencies if there were no association between the variables.

In the context of the Chi Square test, expected frequencies are calculated based on the assumption that the null hypothesis is true, meaning there is no significant difference between the groups being studied. This allows researchers to determine whether the observed results deviate significantly from what would be expected purely by chance. A large discrepancy between observed and expected frequencies indicates that the null hypothesis may be rejected.

The other options do not focus on expected frequencies in the same way. Qualitative analysis generally deals with non-numeric data and does not involve hypothesis testing in the context of expected frequencies. Factor analysis is a technique used to identify underlying relationships between variables, rather than testing hypotheses with frequencies. Correlation analysis focuses on the relationship between two numerical variables and the strength or direction of their association, without dealing with expected frequencies. Thus, the Chi Square test is the only method listed that directly utilizes expected frequencies for hypothesis testing.