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Principles of Biostatistics ANOVA

Principles of Biostatistics ANOVA. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level. ANOVA (Analysis of Variance) Assumptions:

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Principles of Biostatistics ANOVA

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  1. Principles of BiostatisticsANOVA

  2. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  3. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level. • ANOVA (Analysis of Variance) • Assumptions: • Samples are independent (within and among groups) • Population variances are equal • Populations are normally distributed

  4. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  5. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  6. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  7. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  8. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  9. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  10. Table shows weight gains for mice on 3 diets. Test the following hypothesis at the α = 0.05 sig level.

  11. Calculating the p-value

  12. Post-hoc Tests

  13. Post-hoc Tests

  14. Post-hoc Tests • Assumptions • Samples are independent • Population variances are equal • Populations are normally distributed • Not paired samples

  15. Estimating the Pooled Variance

  16. Back to the Post-hoc Tests

  17. Post-hoc Confidence Interval

  18. Post-hoc Summary

  19. SPSS Output

  20. Bonferroni’s Correction • Example • A study has 3 groups. • 3 comparisons must be made. • 1 to 2, 1 to 3, 2 to 3 • If the pairwise error rate is 5%, • approximate the overall error rate • Answer: 15%

  21. Bonferroni’s Correction • Example • A study has 4 groups. • 6 comparisons must be made. • 1 to 2, 1 to 3, 1 to 4, • 2 to 3, 2 to 4, 3 to 4 • If the pairwise error rate is 5%, • approximate the overall error rate • Answer: 30%

  22. Bonferroni’s Correction • Example • A study has 3 groups. • 3 comparisons must be made. • 1 to 2, 1 to 3, 2 to 3 • If the overall error rate is 5%, • approximate the pairwise error rate • Answer:

  23. Bonferroni’s Correction • Example • A study has 4 groups. • 6 comparisons must be made. • 1 to 2, 1 to 3, 1 to 4, • 2 to 3, 2 to 4, 3 to 4 • If the overall error rate is 5%, • approximate the pairwise error rate • Answer:

  24. Formula for # of Comparisons

  25. Post-hoc Confidence Intervals with Bonferroni’s Correction

  26. Post-hoc Confidence Intervals with Bonferroni’s Correction

  27. Post-hoc Confidence Intervals with Bonferroni’s Correction

  28. SPSS Output

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