1. Goodness of Fit and Chi- square test The application of contingency table

2. Goodness of fit Test whether a priori probability is correct or not Compare the real samples with the theoretical expected occurrences

3. Goodness of fit test Expected results for a binomial distribution Real samples

4. Chi-square test for fitness ( ∵ sum of pi must be equal to 1, so the d.f. reduced by 1)

5. Asymptotical proof

6. Asymptotically approaching to the chi-distribution by simulation By the law of large number, the binomial distribution Xi will make the right tail distribution of T approaching to the χ2 distribution See chi-test.xls

7. Goodness of fit test with some unspecified parameters

8. Contingency table The case of independence

9. Independence test in the contingency table

10. Empirical approach Real occurrences Expected results under H0 is true

11. Comparison Two-way ANOVA without duplicated observations Contingency table

12. Homework #4 Problem 6, 10, 21, 24