# THE MAXIMUM F -RATIO AS A SHORT-CUT TEST FOR HETEROGENEITY OP VARIANCE

1. INTRODUCTORY The most useful form of the well-known test for heterogeneity of variances at present in use is Bartlett's (1937) modification M = -21og e ^ of Neyman & Pearson's (1931) Lx test and is given by tfio&{tf-i2 â,,?}-Ev.log.af, (1) M = where the k variance estimates sf (t = 1,2, ...,k) are respectively based on vt degrees of freedom and N â 2 vt. Although tables of the percentage points of M, based on an adequate approximation to its distribution (Hartley, 1940), are available (Thompson & Merrington, 1946), the computation of M is comparatively laborious and often a deterrent in a rapid survey of data. It is, therefore, the purpose of this paper to investigate the use of the ratio of the largest of the a\ to the smallest in the set, say Fmt& = s2max./5?min. a* a short-cut substitute for M. Clearly, this maximum F ratio can be roughly assessed at a glance and can be gauged against tables of percentage points provided here (Table 3) for a test of significance ' without computation '. The loss ia power compared with the M test is calculated under certain assumptions and is found to be negligible http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrika Oxford University Press

## THE MAXIMUM F -RATIO AS A SHORT-CUT TEST FOR HETEROGENEITY OP VARIANCE

Abstract

1. INTRODUCTORY The most useful form of the well-known test for heterogeneity of variances at present in use is Bartlett's (1937) modification M = -21og e ^ of Neyman & Pearson's (1931) Lx test and is given by tfio&{tf-i2 â,,?}-Ev.log.af, (1) M = where the k variance estimates sf (t = 1,2, ...,k) are respectively based on vt degrees of freedom and N â 2 vt. Although tables of the percentage points of M, based on an adequate approximation to its distribution (Hartley, 1940), are available (Thompson & Merrington, 1946), the computation of M is comparatively laborious and often a deterrent in a rapid survey of data. It is, therefore, the purpose of this paper to investigate the use of the ratio of the largest of the a\ to the smallest in the set, say Fmt& = s2max./5?min. a* a short-cut substitute for M. Clearly, this maximum F ratio can be roughly assessed at a glance and can be gauged against tables of percentage points provided here (Table 3) for a test of significance ' without computation '. The loss ia power compared with the M test is calculated under certain assumptions and is found to be negligible

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