1 / 31

Module 18: One Way ANOVA

Module 18: One Way ANOVA. This module begins the process of using variances to address questions about means. Strategies for more complex study designs appear in a subsequent module. Reviewed 11 May 05 /MODULE 18. Independent Random Samples from Two Populations of Serum Uric Acid values.

devi
Download Presentation

Module 18: One Way ANOVA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Module 18: One Way ANOVA This module begins the process of using variances to address questions about means. Strategies for more complex study designs appear in a subsequent module. Reviewed 11 May 05 /MODULE 18 18 - 1

  2. Independent Random Samples from Two Populations of Serum Uric Acid values 18 - 2

  3. Serum Acid SS (Total) Worksheet 18 - 3

  4. SS (Within) and SS (Among) worksheet 18 - 4

  5. SS (Within) = SS (sample 1) + SS (sample 2) = 0.824 + 1.669 = 2.490 SS (Within) = 2.49 18 - 1

  6. 1. The hypothesis: H0: 1 = 2 vs H1: 1  2 2. The assumptions: Independent random samples , normal distributions, 3. The -level : = 0.05 4. The test statistic: ANOVA 5. The rejection region: Reject H0: 1 = 2 if 18 - 7

  7. 6. The result: 7. The conclusion: Reject H0: Since F = 10.86 > F0.95(1,18) = 4.41 18 - 8

  8. Testing the Hypothesis that the Two Serum Uric Acid Populations have the Same Mean 1. The hypothesis: H0: 1 = 2vs H1: 1  2 2. The -level: = 0.05 3. The assumptions: Independent Random Samples Normal Distribution 4. The test statistic: 18 - 9

  9. 5. The reject region:Reject H0 if t is not between ± 2.1009 6. The result: 7. The conclusion:Reject H0 : 1 = 2since t is not between  2.1009 18 - 10

  10. Example 2 18 - 11

  11. 18 - 12

  12. SS(Among) = 11.236 + 25.921 + 22.201 - 57.685 = 1.673 SS(Within) = 0.824 + 1.669 + 1.169   = 3.662 SS(Total) = 1.673 + 3.662 = 5.335 18 - 13

  13. The hypothesis: H0: µ1=µ2=µ3 ,vs. H1: µ1≠ µ2≠ µ3 • 2. The assumptions: Independent random samples normal distributions • 3. The -level : = 0.05 • 4. The test statistic: ANOVA Testing the Hypothesis that the Three populations have the same Average Serum Uric Acid Levels 18 - 14

  14. 18 - 15

  15. Example 3 18 - 16

  16. 18 - 17

  17. SS(Among) = 111,936 + 94,478 + 93,123 - 299,001      = 536.47  SS(Within) = 708 + 202 + 1,134   = 2,043.70   SS(Total) = 536 + 2,043 = 2,580.17 18 - 18

  18. The hypothesis: • 2. The assumptions: Independent random samples normal distributions • 3. The -level : = 0.05 • 4. The test statistic: ANOVA Testing the Hypothesis That the Three Populations Have the Same Average Blood Pressure Levels 18 - 19

  19. 18 - 20

  20. 18 - 21

  21. For Group 1, first child, Individual effect = = 100 - 105.8 = - 5.8 100 = 99.83 + 5.97 + ( -5.80) Xij = + i + ij Yij = + i + ij Individual Value = Overall Mean + Group Effect + Individual Effect Group Effect Random Effect 18 - 22

  22. Pulmonary Function Equipment Comparison 18 - 23

  23. 18 - 24

  24. All Four 18 - 25

  25. Example: AJPH, Sept. 1997; 87 : 1437 18 - 26

  26. ANOVA for Anxiety at Baseline 18 - 27

  27. ANOVA for Psychosocial Adjustment to illness at 3 months 18 - 28

  28. Example: AJPH, August 2001; 91:1258 18 - 29

  29. 18 - 30

  30. 18 - 31

  31. 18 - 32

More Related