LectureNov5

LectureNov5 - BME 423 Lecture Notes - Nov. 5, 2008 Multiple...

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1 Multiple Treatments in Same Subject BME 423 Lecture Notes - Nov. 5, 2008 II. New ANOVA Framework A. New Notation B. Squared Deviation Formulation C. Example III.Repeated Measures ANOVA A. Experiment Framework B. Partitioning Variability C. Procedure Glantz Chapt. 9, pp 330-352 Appendix A, p. 467 Paired t Test - Example 27 . 4 41 . 2 3 . 10 = = = d s d t Platelet aggregation before and after smoking a cigarette - % change (2,4,10,12,16, 15 ,4 ,27 ,9 , 1 ,15) i d = 11 0 n ν = −= n=11 10.3% d = 8.0% d s = 2.41% d d s s n == 0.01 4.27 (10) 3.17 tt => = Reject null hypothesis: 0.01 P <
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2 2. Variance of each group 12 1 1 ,,, n mi i x xx x x n = ⎛⎞ = ⎜⎟ ⎝⎠ Summary of ANOVA (F Test) Experiment: m - # of treatment groups n - # number of subjects per group Null Hypothesis: RV X is measured H0: No effective treatment on X () 2 22 2 2 1 1 1 n i s ss s x x n = =− 1. Mean of each group 1 1 m wit i i s s m = = 3. Calculate the within groups variance 1 1 m i i Xx m = = 4. Compute the overall (grand) mean 6. Calculate the between groups variance 2 2 X bet ns s = 5. Compute standard error of the mean 2 2 1 1 1 m i X i s xX m =
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3 7. Compute the F Statistic 2 2 bet wit s F s = 1 (1 ) n d m mn ν = =
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LectureNov5 - BME 423 Lecture Notes - Nov. 5, 2008 Multiple...

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