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Psychometrika

, Volume 7, Issue 3, pp 195–212 | Cite as

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

  • Fei Tsao
Article

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.

Keywords

Public Policy General Solution Statistical Theory Complete Analysis Statistical Hypothesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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.Google Scholar
  2. 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:Google Scholar
  3. 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).Google Scholar
  4. 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.Google Scholar

Copyright information

© Psychometric Society 1942

Authors and Affiliations

  • Fei Tsao
    • 1
  1. 1.Department of Educational ResearchUniversity of TorontoCanada

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