LectureOct13

# LectureOct13 - BME 423 Lecture Notes - Oct. 13, 2008 Types...

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Types of Error in Inferences and Power of a Statistical Test BME 423 Lecture Notes - Oct. 13, 2008 III. What Determines a test’s Power A. Size of Type I Error B. Size of Treatment effect C. Population Variability D. Number of Samples IV. Sample Size for t Test Glantz p 179-204

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Given a method that produces <0.05 chance of false positive what is the chance of a false negative? t=2.101 111/200=.56 89/200=.44 Power of the Test
Power of the Test : Chance of detecting a real difference of a given size Two Types of Errors

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What Determines a Test’s Power A. Size of Type I Error Power=0.56 Power=0.27 () ' 12 22 ' 200 2.236 200 10 200 10 t nn t μμ σσ = + == + 0.05 α= 0.01 α
What Determines a Test’s Power B. Size of Treatment Effect () ' 22 100 1.118 200 10 200 10 t == + Power=0.56 Power=0.99 ' 400 4.472 200 10 200 10 t + Power=0.17

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Power Function vs Size of Treatment Effect
What Determines a Test’s Power C. Population Variability () ' 12 22 2 1 ' ' 2 2 2 t nn t n n t n μ σσ μμ σ δσ δ = + −− == +

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What Determines a Test’s Power D. Sample Size () ' 22 200 3.162 200 20 200 20 t == + Power=0.83 ' 12 t nn μ σσ = +

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' 2 2 n t n δσ δ σ φ == = Power Function for T Test
Calculating Sample Size for t Test - Example

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## LectureOct13 - BME 423 Lecture Notes - Oct. 13, 2008 Types...

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