What is the chi-square test and what does it measure?

What is the chi-square test and what does it measure?

• A. a parametric statistics test; it measures mean differences
• B. a non-parametric statistics test; it measures how well observed frequencies match a hypothesized distribution
• C. a non-parametric test measuring correlation
• D. a parametric test for variance

Answer: (B)

The chi-square test is a non-parametric method that assesses whether observed categorical frequencies align with what we’d expect under a specific hypothesized distribution. It works by comparing each category’s observed count to its expected count, then summing the squared differences divided by the expected counts: sum of (O − E)² / E. This single statistic is then interpreted using the chi-square distribution to decide if the deviations are likely due to chance. This test is used in two common ways: a goodness-of-fit test, where a single categorical variable is compared to a proposed distribution, and a test of independence in a contingency table, where two categorical variables are assessed for association. Because it relies on counts in categories rather than parameters estimated from a normal distribution or on means/variances of continuous data, it’s non-parametric. It’s not about mean differences or variance, and it does not measure a correlation between continuous variables.

The chi-square test is a non-parametric method that assesses whether observed categorical frequencies align with what we’d expect under a specific hypothesized distribution. It works by comparing each category’s observed count to its expected count, then summing the squared differences divided by the expected counts: sum of (O − E)² / E. This single statistic is then interpreted using the chi-square distribution to decide if the deviations are likely due to chance.

This test is used in two common ways: a goodness-of-fit test, where a single categorical variable is compared to a proposed distribution, and a test of independence in a contingency table, where two categorical variables are assessed for association. Because it relies on counts in categories rather than parameters estimated from a normal distribution or on means/variances of continuous data, it’s non-parametric.

It’s not about mean differences or variance, and it does not measure a correlation between continuous variables.