Lesson 6 Nonparametric Test 2009 Ta
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This document provides an outline and examples for teaching nonparametric tests. It discusses the differences between parametric and nonparametric tests, outlines four key nonparametric tests (Mann-Whitney U, Wilcoxon Signed-Rank, Kruskal-Wallis, Wilcoxon Rank Sum), and provides three examples applying these tests to analyze medical data comparing treatment groups or measuring values before and after an intervention. Exercises are also provided for students to practice applying these nonparametric tests.
Lesson 6 Nonparametric Test 2009 Ta
- 1. Nonparametric Test Teaching Assistant: Zuo Xiaoyu Chapter 7
- 2. Outline Summary of the hypothesis testing methods learned so far Computer experiments of different types of Nonparametric test based on rank. Interclass practices
- 3. Questions for this chapter What is nonparametric test? What is the difference between parametric test and nonparametric test? When should we use parametric test and when should we use nonparametric test? Different designs for nonparametric test we have learned?
- 4. Summary of methods FLOWCHART
- 5. Several points for the flowchart
- 6. 1. Different types of data Cardinal data (continuous variable) Ordinal data (ordinal variable) Nominal data (categorical variable)
- 7. 2. Decision rule of nonparametric test Assumptions met? follows normal distribution , ; homogeneity of variances, . LEVENE’S VARIANCE EQUALIT TEST NORMALITY TEST OR Q-Q PLOT For 3 or more samples
- 8. 3. Comparison of parametric test and nonparametric test under different design: Mann-Whitney U Test(2 independent samples) Wilcoxon Signed-Rank Test (2 related samples) Kruskal-Wallis Test (k independent samples) Two independent sample t -test Paired sample t -test ANOVA Wilcoxon Rank Sum Test
- 9. 4. Multiple comparison problem For parametric test: LSD- t test SNK- q test Bonferroni Correction for α For nonparametric test based on rank: Bonferroni Correction for α
- 10. Computer experiment section Three examples
- 11. Example 7.1 A senior registrar in the rheumatology clinic of a district hospital has designed a clinical trial of a new drug for rheumatoid arthritis. 20 patients were randomized into two groups of ten to receive either the standard therapy A or a new treatment B. The plasma globulin fractions after treatment are listed in table 7.1
- 12. Tabel 7.1 plasma globulin fraction after randomization to treatments A or B We wish to test whether the new treatment has changed the plasma globulin, and we are worried about the assumption of Normality. Design? Steps of analysis? Data: EX-7.1.SAV 45 40 39 39 42 40 38 27 28 45 TreatmentB 33 35 30 32 31 36 41 29 26 38 TreatmentA
- 13. Two Independent Samples Normality met? Equal variance met? Data: EX-7.1.SAV
- 14. 7.1.2 Data File Variable Name: globulin ; Variable Label: Plasma globulin fraction; Variable Name: group Value Label(1:treatment A; 2:treatment B)
- 15. 7.1.3 Procedure From the menus, choose: Analyze Non-parametric Test 2 independent samples, open “Two-Independent-Sample Test” dialog box.
- 16. 7.1.3 Procedure In “Two-Independent-Sample Test” dialog box: Click on variable globulin to highlight it, move it to the “Test variable List” box by clicking the right-pointing arrow between the boxes; Click on variable group to highlight it, move it to the “Grouping Variable” box by clicking the right-pointing arrow between the boxes; Click on button, type “1” in the box of Group 1 and type “2” in the box of Group 2, click on button; Click on button.
- 17. 7.1.4 Output and Interpretation The data is analyzed by the Mann-Whitney U test. The results indicate that there is a statistically significant difference in plasma globulin fraction between treatment A and treatment B (z=2.01, p=0.045). You can determine which group has the higher rank by looking at “Mean Rank’. The mean rank of treatment B is larger than that of treatment A.
- 18. Triglycerides are blood constituents that are thought to play a role in coronary artery disease. To see whether regular exercise could reduce triglyceride levels, researchers measured the concentration of triglycerides in the blood serum of 7 male volunteers, before and after participation in a 10-week exercise program. The results are shown in table 7-2. note that there is considerable variation from one participant to another . For instance, participant 1 had relatively low triglyceride levels both before and after, while participant 3 had relatively high levels. 7.2 Example
- 19. Table 7-2 Serum Triglycerides (mmol/L) Design? Steps of analysis? Data: EX-7.2.SAV 1.51 1.09 1.20 1.43 1.47 1.03 0.57 After 1.60 1.18 2.98 2.14 3.14 1.13 0.87 Before 7 6 5 4 3 2 1 Participant
- 20. Two Related Samples (paired design) Normality met? Equal variance needed? Data: EX-7.2.SAV
- 21. 7.2.2 Data File Variable Name: before; after.
- 22. 7.2.3 Procedure From the menus, choose: Analyze Non-parametric Test 2 related samples”, open “Two-Related-Sample Tests” dialog box.
- 23. 7.2.3 Procedure In “Two-Related-Sample Tests” dialog box: Click on variable before and after to highlight them, move them together to the “Test Pairs List” box by clicking the right-pointing arrow between the boxes; Choose “Wilcoxcon” in Test Type (default); Click on button.
- 24. 7.2.4 Output and Interpretation The data is analyzed by the Wilcoxon Signed-Rank Test. The results indicate that there is a statistically significant difference in Serum Triglycerides before and after participation in a 10-week exercise program (z=2.37, p=0.018).
- 25. 7.3 Example DNA content in gastric mucosal cells among 4 kinds of persons are shown in table 7-3. Is there a significant difference in DNA content in gastric mucosal cells among 4 kinds of persons. Table 7-3 DNA content in gastric mucosal cells among 4 kinds of persons 16.4 18.8 19.4 15.6 21.1 23.1 23.9 19.9 22.9 27.2 28.6 25.1 AGC 27.2 13.4 23.5 20.6 32.2 17.1 23.4 17.8 20.3 EGC 14.1 16.4 12.0 13.0 14.6 14.7 16.5 17.2 13.9 GMH 12.8 12.2 13.7 10.7 9.0 13.4 11.9 H DNA content (A.U) Kinds
- 26. k Independent samples Data: EX-7.3.SAV Normality met? Equal variance needed?
- 27. 7.3.2 Data File Variable Name: dna ; Variable label (DNA content A.U) Variable Name: group ; Value label (1:healthy; 2: hyperplasia; 3: early cancer 4: advanced cancer)
- 28. 7.3.3 Procedure From the menus, choose: Analyze Non-parametric Test k independent samples, open “Test for Several Independent Samples” dialog box. In “Test for Several Independent Samples” dialog box: Click on variable dna to highlight it, move it to the “Test Variable List” box by clicking the right-pointing arrow between the boxes; Click on variable group to highlight it, move it to the “Grouping Variable” box by clicking the right-pointing arrow between the boxes; Click on button, type “1” in the box of Minimum and type “4” in the box of Maximum, click on button; Click on button.
- 30. 7.3.4 Output and Interpretation The data is analyzed by the Kruskal-Wallis Test. The results indicate that there was a statistically significant difference in DNA content in gastric mucosal cells among 4 kinds of persons (chi-square=24.7, P<0.001).
- 32. Exercise 1 14 newborn infants were grouped into 4 categories according to their mother’s smoking habit. A: smoking more than 20 cigarettes per day; B: smoking less than 20 cigarettes per day; C: ex-smoker; D: never smoking. Their weights are listed in Table 12.7.
- 34. Exercise 2
- 35. Exercise 3 The investigator carry out the experiment to compare the anti-tumor effects of three anti-tumor drugs A, B, C on mice sarcoma （肉瘤） . 15 mice of the same race were selected and three anti-tumor drugs A, B, C randomly allocated into 3 mice within the same block.
- 36. With the observations of sarcoma’s weight, the experiment results are shown in Table11.11. Please test if the effects of three anti-tumor drugs are different.
- 38. Assignment P 204 N. 1 N. 3 Hand your homework on Monday afternoon (in class) or Tuesday noon (3th floor, the building of Public Health School)
- 39. Thank you!!!