Conflict among testing procedures in a linear regression model

Daniel F. Kohler

Expert InsightsPublished 1981

It is generally known that an inequality relation exists between different test statistics used for testing linear restrictions. In this paper it is shown that this inequality relation is due to the fact that the test statistics have different distributions whenever the null hypothesis is not true. However, since they all converge to the same asymptotic distribution if the null hypothesis is true, we are led to using the same critical value. As a consequence the rejection probabilities differ, implying different power for the tests.

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Kohler, Daniel F., Conflict among testing procedures in a linear regression model. Santa Monica, CA: RAND Corporation, 1981. https://www.rand.org/pubs/papers/P6691.html.
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