Goodness-of-fit tests whether one categorical variable's observed frequencies match a specific expected distribution (like whether a die is fair). Test of independence tests whether two categorical variables are related, using a contingency table (like whether product preference depends on age group).
What does a small expected count mean for my results?+−
The chi-square approximation becomes unreliable when expected frequencies are too small — the standard rule of thumb is every expected cell count should be at least 5. With smaller expected counts, consider combining categories or using Fisher's exact test instead.
Is a significant chi-square result the same as a strong relationship?+−
No — statistical significance means a relationship is unlikely to be pure chance, not that it's large or practically important. A large sample can make even a weak association statistically significant. Pair a significant result with an effect size measure like Cramér's V before judging practical importance.
Can chi-square tell me which variable causes which?+−
No — like correlation, a significant test of independence shows an association between two categorical variables, not which one (if either) causes the other, or whether a third variable explains both.