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Chapter 07 Chi Square

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ghalan

1. The document discusses Chi-square tests for categorical variables, including tests for goodness of fit, comparing proportions between independent samples, and contingency tables. 2. Examples are provided to illustrate Chi-square tests for comparing the results of two medical testing methods and evaluating whether patient outcomes are independent of a treatment. 3. Requirements for using Chi-square tests are outlined, along with alternative tests like Fisher's exact test that are used when Chi-square assumptions are not met.

Health & MedicineBusinessTechnology
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[object Object],[object Object]
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 ）
 2 distribution
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
[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]
Example 6.1 ,[object Object]
ν ＝ 1
 2 test and Z test ,[object Object]
Correction for continuity ,[object Object]
Fisher’s exact test ,[object Object],[object Object]
Example 6.9
Statistical description
Statistical inference
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 Trt A Trt B Total + - +  11 (a)  12 (b)  r1 -  21 (c)  22 (d)  r2 Total  c1  c2 1.0
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 group + － I II III IV V … … … … … … … … … … VI … …
6.4.3 Measurement of association for R×C table
Pearson contingency coefficient
[object Object],[object Object],[object Object],[object Object],[object Object]
Chapter 07 Chi Square

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Chapter 07 Chi Square

  • 1.
  • 2.
  • 3.
  • 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
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 12.
  • 13.
  • 14.
  • 18.
  • 19. test for independence between two binary variables  2 =173.74 Example 6.2 12/80=15% 172/180=95%
  • 20.
  • 21.
  • 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
  • 29.