371chapter8f2011a - Chapter 8 *Statistical Power (Optional)...

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Chapter 8 *Statistical Power (Optional) 8.1 Tests of Hypotheses Revisited As discussed earlier, a standard practice in research consists of: 1. Select null and alternative hypotheses. 2. Specify the signiFcance level of the test, α .(R em em b e rt h a tt h es i g n i F c a n c el e v e li st h e probability the test rejects a true null hypothesis.) 3. Collect and analyze data; decide whether or not to reject the null. In this chapter we will consider the following two questions .Inp r a c t ic e ,theF r s tque s t ioni s hugely more applicable than the second. 1. Just because we fail to reject the null, how good should we feel about continuing to assume it is true? 2. Just because we reject the null, does it really mean the nullisnogood? Rather than try to explore these questions in a general mathematical way, I will begin with several examples. To Fx ideas, consider our ±isher’s test to investigate whether p is constant in a sequence of trials that might be BT. Suppose we obtain the following data.
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Table 2 Success Failure Total ˆ p First Half 3 0 3 1.00 Second Half 0 3 3 0.00 Total 3 3 6 At the other extreme (and note that these data are a bit silly inpractice),considerthefollowing table. Table 3 Success Failure Total ˆ p First Half 50,500 49,500 100,000 0.505 Second Half 50,000 50,000 100,000 0.500 Total 100,500 99,500 200,000 This table gives a P-value of 0.0256, which would lead to rejecting the null for α =0 . 05 .Bu tI cannot think of any scienti±c problem for which I would want toconcludethat p has changed! The ˆ p ’s are so very close that I believe the assumption of constant p would be scienti±cally useful.
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This note was uploaded on 12/10/2011 for the course STATS 371 taught by Professor Hanlon during the Fall '11 term at University of Wisconsin.

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371chapter8f2011a - Chapter 8 *Statistical Power (Optional)...

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