, Volume 6, Issue 5, pp 309–316

Synthesis of variance

  • Franklin E. Satterthwaite

DOI: 10.1007/BF02288586

Cite this article as:
Satterthwaite, F.E. Psychometrika (1941) 6: 309. doi:10.1007/BF02288586


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.

Copyright information

© Psychometric Society 1941

Authors and Affiliations

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

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