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Hypothesis Test
Conclusion
Test Says
Medical researchers usually give these four instances name, as summarized in the following
table:
Truth
Have Don‟t Have
Positive True Positive False Positive
(Type II Error)
Negative False Negative True Negative
(Type I Error)
As can be seen, the green cells represent accurate results (true results) and the red cells represent
inaccurate results (false results).
As a patient, you would probably be quite upset (devastated, even) if you received false results
for a terrible condition, such as X!
In a hypothesis test, we are up against the same dilemma: our test result can be either positive or
negative. The truth may or may not be accurately represented. Let‟s modify our table slightly to
represent the hypothesis test scenario:
Don‟t
Reject
Truth
True
True Positive
False
False Positive
(Type II Error)
Reject
False Negative
(Type I Error)
True Negative
In reality, we shouldn‟t reject (make it appear false), when it is true. If we do, we have a false
negative on our hands. Similarly, we shouldn‟t not reject (make it appear true), when it is
false. These are labeled Type I and Type II errors, respectively.
How Do We Avoid Erroneous Conclusions
Unfortunately, we are not omniscient. Thus, we can never be sure that our conclusions are
accurate. If we knew, there would be no testing necessary!
On the flipside, we can determine how large of an error rate we require. Earlier, we mentioned
that we will reject when the probability of observing something as or more extreme as what
we have observed is “small.” This value of small fully determines our probability of a Type I
error. As researchers, it is our duty to set this value. This probability of a Type I error is called
the criterion, or alpha-level, and is denoted with the Greek letter alpha, .
Criterion/Alpha-Level
Statistics for Decision-Making in Business © Milos Podmanik Page 213