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Hypothesis Test
Conclusion
Since your decision criteria, or the numerical figure that we later calculate to decide whether or
not to reject, will be extremely stringent and difficult to achieve. If this is the case, then you
almost never reject the null hypothesis!
Okay, so if you very rarely reject the null hypothesis, then you are also potentially committing
another act of error: not rejecting the null hypothesis, even though it may be false. That is, you
increase the likelihood of a Type II error. Recall that,
( ) ( )
We can see here that failing to reject results in potentially failing to reject it even when it
should be rejected! Unfortunately, there is no free lunch in hypothesis testing.
Truth
Don‟t
Reject
True
False Negative
(Type II Error)
Reject
True Positive
Though we cannot yet easily provide numerical support for this claim (which certainly makes
sense), we will make the following preliminary conclusion:
Type II Error -
The probability of a Type II error, denoted , is inversely proportional to , the probability of a
Type I error. That is, decreasing will increase .
Important Caution
Students are often confused that the probability of rejecting when is true and the
probability of failing to reject when is true sum to 1. After all, these two possibilities are
only two of the four possible results in a test decision.
However, keep in mind that these are the percentages of time we reject and fail to reject out of all
the times that is true! This out of only one column total, not the entire sample space.
Statistics for Decision-Making in Business © Milos Podmanik Page 215