Z-Test vs. Chi-Square — What's the Difference?

Z-Test is a statistical test that primarily focuses on comparing means. Specifically, it's employed when one wants to know if a sample's mean is significantly different from a known population mean. Given that the population standard deviation is known, Z-Test can effectively discern this difference. On the other hand, Chi-Square is a test of independence or association. It measures if there is a significant association between two categorical variables, making it highly applicable in contingency table analyses.

Both Z-Test and Chi-Square are integral in hypothesis testing. However, where Z-Test deals with means and requires knowledge of the population standard deviation, Chi-Square examines relationships between categorical variables. The latter does this by comparing the observed frequencies in different categories with the frequencies one would expect under certain assumptions.

In practice, a researcher might use a Z-Test to determine if a new teaching method has led to different test scores for a group of students, comparing it to a population mean. In contrast, the same researcher could use Chi-Square to see if there's an association between gender and preference for a teaching method among a group of students.

Consequently, while Z-Test and Chi-Square can sometimes be used in tandem, their primary functions in research are distinct. The former handles means, and the latter, categorical variables. Both, however, enable researchers to draw meaningful conclusions from data.