# Lecture08 - 22 May 2003 Biostatistics 6650-L8 1 Todays...

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22 May 2003 Biostatistics 6650--L8 1

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22 May 2003 Biostatistics 6650--L8 2 Today’s Schedule Hypothesis Testing: one sample general approach/procedure example: one sample normal, σ known P-values Relationship between hypothesis testing and confidence intervals
22 May 2003 Biostatistics 6650--L8 3 Hypothesis Testing: General Goal: Find evidence in support of a hypothesis Tools data from experiments based on samples assume samples are representative of the population ideally random probability models

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22 May 2003 Biostatistics 6650--L8 4 Hypothesis Testing: General Hypothesis testing provides an “objective framework” for making decisions based on probabilistic models, as opposed to subjective impressions-- Rosner
22 May 2003 Biostatistics 6650--L8 5 Hypothesis Testing: General Example: Wish to determine if treatment of Graves’ ophthalmopathy patients with orbital radiotherapy is effective at reducing proptosis. Develop a hypothesis about the parameter of interest Determine a random variable to measure and an appropriate probability model Design and conduct an experiment Make a decision regarding the hypothesis

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22 May 2003 Biostatistics 6650--L8 6 Hypothesis Testing: General Null Hypothesis: Statement about the population parameter( ,p) assumed to be true for the purposes of testing • Denoted by H o Alternative Hypothesis: Statement about the population parameter which is contradictory to the null • Denoted by H a Example: • Ho: = o Ha: < o
22 May 2003 Biostatistics 6650--L8 7 Hypothesis Testing: General Form of null hypothesis Ho: population characteristic=hypothesized value • Ho: = o o =specified value Form of alternative hypothesis Ha: population characteristic < hypothesized value • Ha: < o Ha: population characteristic > hypothesized value • Ha: > o Ha: population characteristic = hypothesized value • Ha: = o

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22 May 2003 Biostatistics 6650--L8 8 Hypothesis Testing: General Example: Orbital Radiotherapy in Graves’ Disease X=proptosis(mm) 6 months after radiotherapy X~N( , 2 ) Want treatment to reduce proptosis, suspect true pre- treatment mean=21.8mm Ho: Ha:
22 May 2003 Biostatistics 6650--L8 9 Hypothesis Testing: General Two possible conclusions from a hypothesis test • Reject H o • Fail to reject H o Note: We never accept Ho--why? Failing to reject Ho is NOT the same as proving Ho is true. “absence of proof is not proof of absence” practically impossible to prove Ho--define “equal”

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22 May 2003 Biostatistics 6650--L8 10 Hypothesis Testing: General Errors Type I error: rejecting Ho, when Ho is true Type II error: failing to reject Ho, when Ha is true =Pr(Type I error), is referred to the significance level of the test =Pr(Type II error), 1- is the power of the test True State of Reality Ho true Ha true Decision made: Do not reject Ho correct error(II) Reject Ho error(I) correct
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Lecture08 - 22 May 2003 Biostatistics 6650-L8 1 Todays...

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