14. Chisquare Tests

Topics and Notes

1. chi-square goodness-of-fit of categorical distributions
• a. Categorical Distribution
•   ■ Cell probabilities (p_i) for corresponding i-th class label
•   ■ Sum to unity: $\sum_{i=1}^k p_i = 1$
• b. Expected versus Observed Frequencies
•   ■ Expected cell frequencies: sample size × cell probabilities - expected frequency table (E)
•   ■ Observed cell frequencies: The actual counts recorded in the data for each category - observed frequency table (O)
• c. Chisquare Goodness-of-fit Test
•   ■ The distance between two frequency tables
$$TS = \sum_{i=1}^k\frac{(O_i-E_i)^2}{E_i}$$
•   ■ Chisquare distribution and chisquare table
2. Chi-square test of independence (optional)
3. Lecture Note
• a. [Lecture Note] Goodness-of-fit test HTML PDF

Learning Resources

1. [Optional] Read section 12.1 of Navidi's textbook
2. Interactive statistics learning apps
   • a. Chi-square Test of Goodness-of-fit INTERACTIVE APPS
   • b. Chi-square Test of Independence INTERACTIVE APPS