# Lec10 - Test results available online tomorrow(around noon...

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Test results : available online tomorrow (around noon)

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Why use one method over the other? confidence intervals and hypothesis testing Tells us something about the magnitude of the difference between the two means Tells us something about the strength of the evidence that the two means are really different
How do we interpret the significance level α ? For example, α = .05 df = 60 The sampling distribution of t s if H 0 is true If H 0 is true , then only 5% of the time will we choose samples that give us a t s in these tails. Pr{reject H 0 when it is actually true} = .05 t test meta-experiment:

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How do we interpret the significance level α ? If we reject the null hypothesis H 0 then there are two possibilities: 1. H 0 is actually false and the means are different; or 2. H 0 is actually true but we are one of the unlucky 5% who rejected H 0 anyway = Error !
What’s the difference between a P- value and a significance level α ? A. A P -value is determined from the data and α is an arbitrary prespecified value B. A P -value is an arbitrary prespecified value and α is determined from the data C. Both are arbitrary prespecified values D. Both are determined from the data ?

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Type I and Type II Errors Erroneously rejecting H 0 when it is true. By choosing a value of α , we are choosing a level of protection against type I errors . α = Pr{reject H 0 } if H 0 is true. You may choose to protect yourself even more against this risk α = .01 (1% risk) α = .001 (.1% risk) Erroneously not rejecting H 0 when it is false. True situation H 0 true H 0 false Our decision Do not reject H 0 Correct Type II error Reject H 0 Type I error Correct
Type II: Not rejecting H 0 when you should have H 0 : Immunotherapy is not effective in enhancing survival. H A : Immunotherapy does affect survival. Which one of these two would be a consequence of a Type II Error: A. Immunotherapy does improve survival, yet the standard chemotherapy continues to be used without the benefits of immunotherapy. B. Widespread use of unpleasant, dangerous and worthless immunotherapy α limits the risk of a Type I error: Rejecting H 0 when it was actually true Example A. Immunotherapy does improve survival, yet the standard chemotherapy continues to be used without the benefits of immunotherapy B. Widespread use of unpleasant, dangerous and worthless immunotherapy The significance level limits the risk of which one of these consequences?

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## This note was uploaded on 11/04/2009 for the course BIO 50935 taught by Professor Bryant during the Fall '09 term at University of Texas.

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Lec10 - Test results available online tomorrow(around noon...

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