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 ) intervals A Φ (X 1 ) Φ (X 2 ) P (X) T=n* P (X) (A-T) 2 /T 1.228- 2 0.00069 0.00466 0.00397 0.5405 3.94143 1.234- 2 0.00466 0.02275 0.01809 2.4601 0.08605 1.240- 7 0.02275 0.08076 0.05801 7.8889 0.10016 1.246- 17 0.08076 0.21186 0.13110 17.8294 0.03859 1.252- 25 0.21186 0.42074 0.20888 28.4083 0.40892 1.258- 37 0.42074 0.65542 0.23468 31.9167 0.80961 1.264- 25 0.65542 0.84134 0.18592 25.2855 0.00322 1.270- 16 0.84134 0.94520 0.10386 14.1244 0.24906 1.276- 4 0.94520 0.98610 0.04090 5.5618 0.43858 1.282- 1 0.98610 0.99744 0.01135 1.5434 0.19130 合 计 - - - - - 6.26692

11. ν ＝ 1

15. Example 6.9

16. Statistical description

17. Statistical inference

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 Trt A Trt B Total + - +  11 (a)  12 (b)  r1 -  21 (c)  22 (d)  r2 Total  c1  c2 1.0

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 group + － I II III IV V … … … … … … … … … … VI … …

27. 6.4.3 Measurement of association for R×C table

28. Pearson contingency coefficient