Chi-square test compares observed frequencies with expected frequencies to determine if differences are statistically significant.
⚠Expected frequencies should be at least 5 in most cells for valid chi-square results.
What is Chi-Square Test?
Chi-square (χ²) test is a statistical test used to determine if there is a significant association between categorical variables. It compares observed frequencies with expected frequencies under the null hypothesis.
Goodness of Fit
Tests if observed distribution matches expected distribution (e.g., dice fairness)
Test of Independence
Tests if two categorical variables are related (e.g., gender vs preference)
Degrees of Freedom
df = (categories - 1) for goodness of fit, df = (r-1)(c-1) for contingency tables
Interpretation
p < 0.05 = significant association, reject null hypothesis
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Frequently Asked Questions
What is chi-square test?▼
Chi-square test determines if there is a significant association between categorical variables. It compares observed frequencies with expected frequencies.
Goodness of fit vs test of independence?▼
Goodness of fit: tests if observed distribution matches expected distribution. Test of independence: tests if two categorical variables are related.
How to interpret chi-square?▼
Higher chi-square = bigger difference between observed and expected. Compare to critical value or use p-value. Small p-value (<0.05) = reject null hypothesis.
What are expected frequencies?▼
Expected frequencies are what we would expect if null hypothesis is true. Calculated as (row total × column total) / grand total for contingency tables.
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