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Tests of statistical hypotheses in the case of unequal or disproportionate numbers of observations in the subclasses

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Abstract

General solutions of the analysis of variance in the case of unequal numbers of observations in the subclasses are presented. If we havek criteria for the classification, there will bek! solutions in making a complete analysis and 2k−1 answers, bearing different meanings, for the sum of squares between subclasses of each criterion. The sum of squares for the interaction of any order, however, will be identical in different solutions of same problem.

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References

  1. Godard, R. H., and Lindquist, E. F. An empirical study of the effect of heterogeneous within-group variance upon certainF-tests of Significance in analysis of variance.Psychometrika, 1940,5, 263–274.

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  2. Jackson, R. W. B. Application of the analysis of variance and covariance method to educational problems. Bulletin No. 11, Department of Educational Research, University of Toronto, 1940. Pp. 103:

  3. Johnson, P. O., and Neyman, J. Tests of certain linear hypotheses and their application to some educational problems.Statistical Research Memoirs, Department of Applied Statistics, University College, London, W. C. 1., 1936,1, 57–93. (See especially equations (6) to (17) on pp. 58–60).

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  4. Welch, B. L. Note of an extension of theL 1 test.Statistical Research Memoris, Department of Applied Statistics, University College, London, W. C. 1., 1936,1, 52–56.

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Authors and Affiliations

  1. Department of Educational Research, University of Toronto, Canada

    Fei Tsao

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  1. Fei Tsao
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Tsao, F. Tests of statistical hypotheses in the case of unequal or disproportionate numbers of observations in the subclasses. Psychometrika 7, 195–212 (1942). https://doi.org/10.1007/BF02288616

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  • DOI: https://doi.org/10.1007/BF02288616

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