Question: A researcher routinely tests using a nominal P(type I error) = 0.05, rejecting H 0 if the P-value 0.05. An exact test using test
A researcher routinely tests using a nominal P(type I error) = 0.05, rejecting H0 if the P-value ≤ 0.05. An exact test using test statistic T has null distribution P(T = 0) = 0.30, P(T = 1) = 0.62, and P(T = 2) = 0.08, where a higher T provides more evidence against the null.
a. With the usual P-value, show that the actual P(type I error) = 0.
b. With the mid-P-value, show that the actual P(type I error) = 0.08.
c. Find P(type I error) in parts (a) and (b) when P(T = 0) = 0.30, P(T = 1) = 0.66, P(T = 2) = 0.04. Note that the test with mid P-value can be conservative or liberal. The exact test with ordinary P-value cannot be liberal.
d. In part (a), a randomized-decision test generates a uniform random variable U from [0, 1] and rejects H0 when T = 2 and U ≤ 5/8 . Show the actual P(type I error) = 0.05. Is this a sensible test?
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a No outcome can give P 05 and hence one never reject... View full answer
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