Expected frequencies are crucial in which of the following tests?

Expected frequencies are foundational in the Chi-Square test because this statistical method is used to assess whether there is a significant association between categorical variables. The Chi-Square test compares the observed frequencies of events in each category with the expected frequencies, which are calculated under the assumption that there is no association between the variables.

In a Chi-Square test, expected frequencies are based on the overall distribution of data and the proportions that would be expected if the null hypothesis were true. The test statistic is then computed using these expected values to determine how much the observed frequencies deviate from what would be expected. A significant difference suggests that an association may exist between the categorical variables being analyzed.

For different statistical methods, such as the T-test, ANOVA, and regression analysis, the concept of expected frequencies does not apply in the same way. Instead, those tests focus on means or relationships among continuous variables, where other statistical measures and assumptions come into play.