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Raising the Surprise Probability
One obvious way to lower the hurdle is
to raise the surprise probability. The hurdle for the Statistical Knowledge
Quiz example is that the mean must exceed 11.13 for a surprise probability of
p = .05. If we were willing to accept a surprise probability of .10--the probability
that we would exceed the hurdle even when the null hypothesis were true--then
the hurdle would be lower. The graphs below show the respective decision
rules (the red numbers at the bottom of each graph) and the corresponding
power for alternative hypotheses.
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Use the scrollbar to find the power for testing other alternative
hypotheses.
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In the left graph, where the surprise probability is 5 percent (only a .05 probability that the mean
would exceed the decision rule if the null hypothesis of guessing were true),
the upper hurdle is 11.1.
If the true mean were 11.5, the statistical power is about .74. However, in the right graph,
the surprise probability is 10 percent (a .10 probability that the mean would exceed the
decision rule if the null hypothesis of guessing were true), the upper hurdle
is lowered to 10.9. Now the statistical power increases to .83, which most
statisticians would find acceptable. Later we will consider whether we are
paying to high a price to lower the hurdle in this way. The price is that
with a higher surprise point
we are more likely to conclude incorrectly that students were doing better
than guessing when they were not.
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File:
© 1999, Duxbury Press.
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