LectureSept21

# LectureSept21 - BME 423 Lecture Notes Sept 21 2009...

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1 Hypothesis Testing Special Case of Two Groups BME 423 Lecture Notes - Sept. 21, 2009 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 Chapt 4: p 73-97 A. Idea

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2 difference in sample means standard error of difference of sample means 12 () xx t s = Define a new statistic - t How to calculate? 22 ,, , x sx s From data: , XX ss nn == Also: But need: x x s 1 2 2 x x s = + Can show: t s =
3 Z XY =+ [] [ ] [ ] [] Z EZ EX Y EX EY μ μμ = ±= ± Recall from Probability Z = or ~( ) ) Xf x Yf y X and Y are independent [ ] x y Y = [( ,) ] (,)(,) (,)()() EhXY hxyf xyd x d y hxyf xf yd x d y ∞∞ −∞ −∞ == ∫∫ [ ] () () E x fx fy d x d y y d x d y −∞ −∞ += + [] ( ) ( ) E x d x y d y −∞ −∞ + () 2 22 2 2 [ ] ( ) [( ) ] ( ) Z Z Z σσ =≡ = =− # Z Recall from Probability Z = or But we want: ) ) X Y fy X and Y are independent [ ] x y Y =

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4 12 22 () xx x x x x t s s ss s nn −− == = + + 2 112 2 (1 ) ) 2 ns s −+ = +− Therefore and s s
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## This note was uploaded on 10/13/2009 for the course BME 423 at USC.

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LectureSept21 - BME 423 Lecture Notes Sept 21 2009...

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