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Biometrika 1971 58(2):393-396; doi:10.1093/biomet/58.2.393
© 1971 by Biometrika Trust
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MISCELLANEA

Miscellanea: On alternative approximate F tests for hypotheses involving variance components

RAYMOND H. MYERS and RICHARD B. HOWE

Medical College of Virginia
Louisiana Polytechnic Institute Ruston, Louisiana

An alternative procedure is given to that presently used for assigning approximate degrees of freedom to the usual ratio of synthetic mean squares which is used as an approximate F statistic in analysis of variance. The standard procedure assigns pseudo degrees of freedom by treating the numerator and denominator separately, approximating each as a X2 distribution and equating the first two moments. Here the statistic is approximated directly as an F statistic. Monte Carlo experiments indicate that if one uses this method, the absolute deviation of the size of the test from that advertised is smaller than that of the standard procedure.

Key Words: Approximate F tests • Approximate degrees of freedom • Linear combinations of variance components • Synthetic mean squares; Analysis of variance


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