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Synthesis of Variance

Published online by Cambridge University Press:  01 January 2025

Franklin E. Satterthwaite
Franklin E. Satterthwaite*
Affiliation:
University of Iowa
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Abstract

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.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 5 , October 1941 , pp. 309 - 316
Copyright
Copyright © 1941 The Psychometric Society

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References

Fisher, R. A. The fiducial argument in statistical inference. Annals of Eugenics, 1936, 6, 391–391.CrossRefGoogle Scholar
Welch, B. L. The significance of the difference between two means when the population variances are unequal. Biometrika, 1938, 29, 350–350.CrossRefGoogle Scholar
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, 1–1.Google Scholar