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Simultaneous confidence intervals for two linear functions of population means when population variances are not equal

Published online by Cambridge University Press:  24 October 2008

Saibal Banerjee
Affiliation:
Indian Statistical Institute, Calcutta

Abstract

It is shown that given k samples of nj units from it is possible to construct simultaneous confidence intervals for two given linear functions of population means, (where cij are known constants), when population variances are not equal.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Banerjee, S.Approximate confidence interval for linear functions of means of k populations when the population variances are not equal. Sankhyā, 22 (1960), 357358.Google Scholar
(2)Banerjee, S.On confidence interval for the two means problem based on separate estimates of variances and tabulated values of t-table. Sankhyā, 23 (1961), 339358.Google Scholar
(3)Dunn, Olive Jean. Estimation of the means of dependent variables. Ann. Math. Statist. 29 (1958), 10951111.CrossRefGoogle Scholar
(4)Ferrar, W. L.Algebra (Oxford University Press, 1953).Google Scholar
(5)McCullough, R. S., Gurland, J. and Rosenburg, L.Small sample behaviour of certain tests of hypothesis of equal means under variance heterogeneity. Biometrika, 47 (1960), 345354.CrossRefGoogle Scholar
(6)Miller, R. G. JrSimultaneous 8tat'z8twal inference (McGraw Hill, 1966).Google Scholar
(7)Scheefe, Henry. A method of judging all contrasts in the analysis of variance. Biometrika, 40 (1953), 87104.Google Scholar
(8)Welch, B. L.The significance of the difference between two means when the population variances are unequal. Biometrika, 29 (1947), 250362.Google Scholar