Lec11 - Suppose a new drug is being considered for approval...

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Suppose a new drug is being considered for approval by the FDA. The null hypothesis is that the drug is not effective. If the FDA approves the drug, what type of error, Type I or Type II, could possibly have been made? A. Type I B. Type II C. Both are possible D. Neither are possible ?
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One-tailed t test If the alternative hypothesis is directional we conduct a one-tailed t test: Step 1. Check directionality : Look at the data and assess whether they deviate from H 0 in the direction specified by H A . (a) If not, then conclude that the P -value is greater than 0.5. (b) if so, proceed to Step 2 . Step 2. Determine P- value : The P -value of the data is the one-tailed area beyond t s . Step 3 . Conclude test : Make a decision at the prespecified significance level α : H 0 is rejected if P . H A : μ 1 > 2 H A : 1 < 2
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Directional vs. nondirectional H A ’s The P- value for a directional alternative hypothesis will be half that of the corresponding nondirectional alternative hypothesis. Sometimes data will lead to the rejection of H 0 using a one-tailed procedure but not using a two-tailed procedure. Example: Niacin supplement for increasing weight gain in lambs H 0 :Niacin is not effective in increasing weight gain ( μ 1 = 2 ) H A :Niacin is effective in increasing weight gain ( 1 > 2 ) H 0 :Niacin is not effective in increasing weight gain ( 1 = 2 ) H A :Niacin is effective in increasing weight gain ( 1 2 ) y 1 = 14 lb and y 2 = 10 lb t s = ( 14 - 10 )- 0 2.2 = 1.82 P -value = 0.043 < 0.05. Therefore, we reject H 0 y 1 = 14 lb and y 2 = 10 lb t s = ( 14 - 10 0 2.2 = 1.82 P -value = 0.086 > 0.05 . Therefore, we cannot reject H 0 It is easier to reject H 0 with a one-tailed test than a two-tailed test
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Directional vs. nondirectional H A ’s In both cases, Pr{reject H 0 when it is actually true} = .05 The interpretation of α is the same. When to choose directional alternatives: 1.If you believe that the effect can’t be in the other direction 2.If you are not interested in deviation in the other direction 3. You can only use a directional alternative if you state H A before seeing the data!
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What do we mean when we say “significant”?
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What do we mean when we say “significant”? A significant difference means we were able to reject the claim that the difference in sample means was caused by chance error P .001 P .45 Small but significant difference Large but not significant difference Serum lactate dehydrogenase level 10 11 s 57 60 y 264 270 n Females Males Body weight (lb) 34 35 s 143 175 y 2 2 n Females Males
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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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Lec11 - Suppose a new drug is being considered for approval...

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