issues-in-hypo

issues-in-hypo - Miscellaneous Issues in Hypothesis Testing...

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Miscellaneous Issues in Hypothesis Testing -. Overall Error Rate -. P(H|D) vs P(D|H) -. Oakes’ Study -. Scale Transformation -. Meta Analysis -. Alternative Approaches to Hypothesis Testing Overall Error Rate in Hypothesis Testing 1. The procedure of hypothesis testing is set up so that the type I error rate is controlled to be equal to " in the long run over repeated hypothetical, imaginary samples: P(Reject H o * H o is true) = " . Obs 1: "Over repeated sample" means that H o is assumed to be true in all such samples. Obs 2: On average, out of 100 samples drawn from the H o population, there will be approximately " (100) cases in which H o is incorrectly rejected.
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2. In reality, however, we do not know whether H o is true or not. Taking into account this uncertainty about Ho, the overall error rate of making incorrect decisions, is then given by P(incorrect decision) = P(accept H 1 * H o is true) P(H o is true) + P(retain H o * H 1 is true) p(H 1 is true) = " P(H o ) + $ (1 - P(H o )) Therefore, to obtain the overall error rate, additional information (i.e., p(H o )) is needed. P(H|D) vs P(D|H) The probability of data D given H o , P(D * H o ), is NOT the same as the probability of H o given the data, P(H o * D). As an illustrated example, consider
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D = "male adult" H o = "US Senate member" For these events, note that P(D * H o ) = 0.98 but P(H o * D) = 0.000001!
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issues-in-hypo - Miscellaneous Issues in Hypothesis Testing...

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