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Newsgroups: bit.listserv.stat-l
Date:         Wed, 26 Aug 1992 15:18:02 EST
From:         "A. NARAYANAN DECISION & INFO. SYSTEMS--855-2665"
              <NARAYANA@UCS.INDIANA.EDU>
Subject:      test of variance homogeneity

In article <9208260018.AA15405@dmsmelb.mel.dms.CSIRO.AU>,
alan@DMSMELB.MEL.DMS.CSIRO.AU writes:
> Levene's test is much less sensitive to non-normality than those of Bartlett,
> Hartley and Cochran, but it does need some correction.   I suggest that you
> look at my Letter to the Editor of Technometrics, vol.14, page 507, 1972,
> and you read the paper:
> Yitnosumarto, S. and O'Neill, M.E. (1986) On Levene's tests of variance
> homogeneity, Austral. J. Statist., vol.28(2), 230-241.

See also

1)  Balakrishnan, N., and Ma, C.W. (1990), "A Comparative Study of Various
    Tests for the Equality of Two Population Variances", J. of Statistical
    Computation and Simulation 35, 41-89.

2)  Brown, M.B., and Forsythe, A.B. (1974), "Robust Test for the Equality
    of Variances", J. of the American Statistical Association 69, 364-7.

3)  Conover, W.J., Johnson, M.E., and Johnson, M.M. (1981), "A Comparative
    Study of Tests for Homogeneity of Variances, with Applications to the
    Other Continental Shelf Bidding Data", Technometrics 23, 351-61.

4)  Olejnik, J.S., and Algina, J. (1988), "Tests of Variance Equality When
    Distributions Differ in Form and Location", Educational and Psychological
    Measurement 48, 317-29.

5)  Tan, W.Y. (1982), "Sampling Distributions and Robustness of t, F and
    Variance-Ratio in Two Samples and ANOVA Models with Respect to Departure
    from Normality", Communications in Statistics - Theory and Methods 11,
    2485-511.

6)  Tiku, M.L. (1982), "Robust Statistics for Testing Equality of Means or
    Variances", Communications in Statistics - Theory and Methods 11, 2543-58.

7)  Tiku, M.L. and Balakrishnan, N. (1984), "Testing Equality of Population
    Variances the Robust Way", Communications in Statistics - Theory and
    Methods 13, pg 2143-59.

8)  Wilcox, R.R. (1990), "Comparing Variances and Means When Distributions
    have Non-Identical Shapes", Communications in Statistics - Simulation 19,
    155-73.

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To this I would like to add:

Ramsey,P.H.(1980) Exact Type 1 Error Rates for Robustness of Student's t
Test with Unequal Variances, Journal of Educational Psychology, 5, 337-349.

Markowski, C.A. and Markowski, E.P. (1990). Conditions for effectiveness of
a preliminary test of variance, American Statistician, 44, 322-326.

There is also a paper to be published in the next issue of ASA proceedings
in the statistical computing section titled,"Evaluating Preliminary Tests
of Variances in Two Normal Populations".

I hope this helps.

Narayanan, A.
Indiana University
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU