Lecture 07 Category Shaoqi Rao Rev

[object Object],[object Object],[object Object],[object Object],Slides adapted from Dr. Zhang Jinxin’s

6.1 Basic logic of  2 test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

6.1.1 Chi-square distribution ,[object Object],[object Object],DF=k-1-# parameters estimating f i For a contingency table, DF=(# rows-1)(# columns-1 ）

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

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

 2 test and Z test ,[object Object]

Correction for continuity ,[object Object]

Fisher’s exact test ,[object Object],[object Object]

6.3 The  2 Tests for Binary Variable under a Paired Design ,[object Object]

test for independence between two binary variables  2 =173.74 Example 6.2 12/80=15% 172/180=95%

6.3.2 Comparison between two sample proportions ,[object Object], 2 =

[object Object],[object Object],[object Object],[object Object],0.05

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

Correction to McNemar test ( f 12 + f 21 <40)  2 =  2 = =0.45

6.4 The  2 Test for R×C Contingency Table

The statistic for hypothesis test  2 = =9.488

6.4.2 Multiple comparison for R×C Table control … … VI … … … … … … … … … … I II III IV V － + group

6.4.3 Measurement of association for R×C table

Pearson contingency coefficient

[object Object],[object Object],[object Object],[object Object],[object Object]

Lecture 07 Category Shaoqi Rao Rev

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