Goodness of Fit Examples

Statistics · Axiom Academy

EXAMPLE Goodness of Fit Examples Master chi-square goodness of fit tests with three complete worked examples Example 1: Testing if a Die is Fair A casino manager suspects a die might be weighted. The die is rolled 120 times with the following results: Test at significance level. Null hypothesis: The die is fair (uniform distribution). Excellent work! You've completed three goodness of fit examples. Here's what we learned: Chi-Square Formula: The test statistic measures how much observed frequencies deviate from expected frequencies. Degrees of Freedom: For goodness of fit tests, df = k - 1 where k is the number of categories. This determines the critical value from the chi-square distribution. Decision Rule: Reject the null hypothesis if . Larger test statistics indicate greater deviation from the expected distribution. Expected Frequencies: For uniform distributions, E = n/k. For other distributions (like Mendelian ratios), use the theoretical proportions times the total sample size. Practical Interpretation: A non-significant result doesn't prove the null hypothesis is true; it means we don't have sufficient evidence to reject it. These techniques apply to any situation where you're testing whether observed categorical data matches an expected distribution. Practice with different scenarios to build confidence!

This is the written version of the interactive lesson above. See the full Statistics course.