July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short Course
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10.2 Errors in Testing
It should be intuitively clear that since sample information is used to test hypotheses about a population parameter, an element of uncertainty is involved in assessing the test results. Hence it is possible to reach a “false conclusion.” The two types of errors encountered are:
Type I Error (TIE): Rejecting H0 when it is actually true.
Type II Error (TIIE): Not rejecting H0 when it is actually false.
In fact, the complete set of possible actions given the status of the null hypothesis are presented in Table 10.1.
Table 10.1 Types of Errors.
The risks associated with wrong decisions are the (conditional) probabilities of committing Type I and Type II Errors:
P (Type I Error) = P (reject H0/H0 true) = α.
P (Type II Error) = P (do not reject H0/H0 false or H1 true) = β.
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