LectureSept22

LectureSept22 - BME 423 Lecture Notes - Sept. 22, 2008...

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Hypothesis Testing Special Case of Two Groups BME 423 Lecture Notes - Sept. 22, 2008 I. Comparing Two Groups A. Idea B. t Test Procedure C. Example – Fasting Glucose D. Example – Halothane vs Morphine II. Also, t Test for One Sample Inference
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A. Idea
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difference in sample means standard error of difference of sample means 12 () xx x x t s = Define a new statistic - t
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How to calculate? 22 12 ,, , xs x s From data: , XX ss nn == Also: But need: () x x s 1 2 2 x xx x s = + Can show: x x t s =
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() 2 22 2 2 [] [ ] ( ) [( ) ] ( ) XY Z Z Z EZ E Z EX Y σσ μ =≡ = =− =+ # ZX Y [ ] [ ] Z EX Y EY μμ = ± = ± Recall from Probability Y = or We want: ~( ) ) Xf x Yf y X and Y are independent [ ] x y Y =
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12 22 () xx t s s ss s nn −− == = + + 2 112 2 (1 ) ( 1 ) 2 ns n s s −+ = +− Therefore and s s However, under the null hypothesis a better estimate for σ Replace with Pooled Variance
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B. t Test Procedure (Student t Test) Experiment: 2 treatment groups # number of subjects groups 1 & 2 Null Hypothesis: RV X is measured 12 0: 1: HH μ μμ =≠ , nn 2. Variance of each group
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LectureSept22 - BME 423 Lecture Notes - Sept. 22, 2008...

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