Ch. 15: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Parametric test

A statistical test that requires specific assumptions about population parameters (like normality and equal variances)

Nonparametric test

A test that does not rely on population assumptions and is used with categorical or non-normal data

Chi-Square test for goodness of fit

A test that checks whether observed frequencies match expected frequencies for one categorical variable

Observed frequency

The actual number of cases counted in each category

Expected frequency

The number of cases predicted for each category if the null hypothesis is true

Chi-square statistic (x²)

A measure of how far the observed frequencies differ from expected frequencies across categories

Chi-square distribution

A positively skewed distribution used as the reference for evaluating chi-square test statistics

Chi-square test for independence

A test that determines whether two categorical variables are related or independent of each other

Independent

Two variables are independent if knowing one gives no information about the other

Cohen’s w

An effect size for the chi-square goodness-of-fit test that measures the size of the discrepancy between observed and expected frequencies

Phi-coefficient

An effect size used when the chi-square test for independence is applied to a 2×2 table

Cramér’s V

An effect size for chi-square tests when the table is larger than 2×2, adjusting for table size