Lecture 07 Category Shaoqi Rao Rev
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1. The document discusses Chi-square tests for categorical variables, including tests for goodness of fit, comparison of proportions between independent samples, and contingency tables. 2. Examples are provided to illustrate Chi-square tests for independence between binary variables, comparison of proportions between paired samples using McNemar's test, and tests on R×C contingency tables. 3. Pre-requisites for Chi-square tests are discussed, including minimum expected cell frequencies and using Fisher's exact test for small sample sizes.
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Lecture 07 Category Shaoqi Rao Rev
- 4. 2 distribution
- 5. 6.1.2 χ 2 Test for Goodness of Fit (Large Sample) Table1 Frequency distribution and goodness of fit based on 136 measurements to the phantom( 体模 ) 6.26692 - - - - - 合 计 0.19130 1.5434 0.01135 0.99744 0.98610 1 1.282- 0.43858 5.5618 0.04090 0.98610 0.94520 4 1.276- 0.24906 14.1244 0.10386 0.94520 0.84134 16 1.270- 0.00322 25.2855 0.18592 0.84134 0.65542 25 1.264- 0.80961 31.9167 0.23468 0.65542 0.42074 37 1.258- 0.40892 28.4083 0.20888 0.42074 0.21186 25 1.252- 0.03859 17.8294 0.13110 0.21186 0.08076 17 1.246- 0.10016 7.8889 0.05801 0.08076 0.02275 7 1.240- 0.08605 2.4601 0.01809 0.02275 0.00466 2 1.234- 3.94143 0.5405 0.00397 0.00466 0.00069 2 1.228- (A-T) 2 /T T=n* P (X) P (X) Φ (X 2 ) Φ (X 1 ) A intervals
- 11. ν ＝ 1
- 15. Example 6.9
- 19. test for independence between two binary variables 2 =173.74 Example 6.2 12/80=15% 172/180=95%
- 22. The Probability Expressions H 0 : c1 = r1 H 1 : c1 r1 Since c1 = 11 + 21, r1 = 11 + 12 , This test becomes: H 0 : 12 = 21 , H 1 : 12 21 1.0 c2 c1 Total r2 22 (d) 21 (c) - r1 12 (b) 11 (a) + - + Total Trt B Trt A
- 23. Correction to McNemar test ( f 12 + f 21 <40) 2 = 2 = =0.45
- 24. 6.4 The 2 Test for R×C Contingency Table
- 25. The statistic for hypothesis test 2 = =9.488
- 26. 6.4.2 Multiple comparison for R×C Table control … … VI … … … … … … … … … … I II III IV V － + group
- 27. 6.4.3 Measurement of association for R×C table