What is the main purpose of calculating expected frequencies?

Calculating expected frequencies is primarily used to evaluate the null hypothesis, particularly in the context of categorical data analysis. When researchers conduct tests like the chi-square test of independence, they are interested in determining whether the observed frequencies of categories in a contingency table differ significantly from what would be expected under the null hypothesis.

The expected frequencies provide a baseline for comparison, representing the distribution of categories that would occur if the null hypothesis were true (e.g., assuming no association between variables). By comparing the observed frequencies with these expected frequencies, researchers can assess whether the deviations are statistically significant, thereby informing conclusions about the relationships between the variables. This serves as a crucial step in hypothesis testing, allowing for a systematic examination of categorical data and understanding whether observed patterns are likely due to chance or indicate a valid effect.