A Significance Paradox
Mark J. Schervish
Significance probabilities (or values) have been used in place of
hypothesis tests as a means of giving more information about the
relationship between the data and the hypothesis than does a simple
reject/don't reject decision. Virtually all elementary statistics
texts cover the calculation of values for hypotheses concerning
the mean of a sample from a normal distribution. Both one-sided
hypotheses and point-null hypotheses are usually discussed. But
there is a third case which is intermediate to the one-sided and
point-null cases, namely the interval hypothesis, which receives no
coverage in elementary texts. We show here that values
for interval hypotheses exhibit a paradoxical sort of behavior which was
actually visible in the one-sided and point-null cases, but which
has been largely ignored in the past.
Keywords: Measure of support, value, one-sided hypothesis,
point-null hypothesis, interval hypothesis, significance probability.
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