The rejection region is the interval, measured in the sampling distribution of the statistic under study, that leads to rejection of the null hypothesis H 0 in a hypothesis test. The rejection region is complementary to the acceptance region and is associated to a probability α, called the significance level of the test or type I error.
MATHEMATICAL ASPECTS
Consider a hypothesis test on a parameter θ. We utilize the statistic T in order to estimate this parameter.
Case 1: One-sided Test (Right Tail)
The hypothesis is the following:
where \( { \theta_0 } \) is the preassigned value for parameter θ.
In a one-sided test (test for the right tail), the rejection region corresponds to an interval limited on the right side of the critical value:
Rejection region \( { =\left[ \text{critical value};\infty \right[ } \), and
Acceptance region \( { =\left] -\infty ;\text{critical...
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REFERENCES
Bickel, R.D.: Selecting an optimal rejection region for multiple testing. Working paper, Office of Biostatistics and Bioinformation, Medical College of Georgia (2002)
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© 2008 Springer-Verlag
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(2008). Rejection Region. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_349
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DOI: https://doi.org/10.1007/978-0-387-32833-1_349
Publisher Name: Springer, New York, NY
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