, Volume 6, Issue 5, pp 309–316 | Cite as

Synthesis of variance

  • Franklin E. Satterthwaite


The distribution of a linear combination of two statistics distributed as is Chi-square is studied. The degree of approximation involved in assuming a Chi-square distribution is illustrated for several representative cases. It is concluded that the approximation is sufficiently accurate to use in many practical applications. Illustrations are given of its use in extending the Chi-square, the Student “t” and the Fisher “z” tests to a wider range of problems.


Linear Combination Public Policy Statistical Theory Representative Case 
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  1. Fisher, R. A. The fiducial argument in statistical inference.Annals of Eugenics, 1936,6, 391.Google Scholar
  2. Welch, B. L. The significance of the difference between two means when the population variances are unequal.Biometrika, 1938,29, 350.Google Scholar
  3. Hsu, P. L. Contribution to the theory of “Student's”t-test as applied to the problem of two samples.Statistical Research Memoirs, 1938,2, 1.Google Scholar

Copyright information

© Psychometric Society 1941

Authors and Affiliations

  • Franklin E. Satterthwaite
    • 1
  1. 1.University of IowaUSA

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