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Biometrika 1975 62(2):359-369; doi:10.1093/biomet/62.2.359
© 1975 by Biometrika Trust
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Optimal allocation in sequential tests comparing the means of two Gaussian populations

THOMAS A. LOUIS

Department of Mathematics, Boston University Massachussets

The invariant sequential probability ratio test used in testing for a difference between the means of two Gaussian populations is set up. The error probabilities for this test are effectively constant over a rich class of data-dependent allocation rules. The additional risk, average sample number plus ({gamma} – 1) timss the expected number of observations to the inferior population, for {gamma} ≥ 1, is introduced and the optimal allocation rule is found for the continuous-time analogue to this problem. Analytical results show this rule to be asymptotically optimal in discrete time, and simulations indicate its near optimal performance for the finite case.

Key Words: Clinical trials • Optimal allocation of observations • Sequential design of experiments • Two-population hypothesis tests


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