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Biometrika 1980 67(2):503-504; doi:10.1093/biomet/67.2.503
© 1980 by Biometrika Trust
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MISCELLANEA

Efron's conjecture on vulnerability to bias in a method for balancing sequential trials

J. MICHAEL STEELE

Department of Statistics, Stanford University

Efron (1971) proposed a method for sequential assignment to treatments or control which is in many ways superior to traditional procedures. To analyse the method's susceptibility to accidental bias a criterion concerning the maximum eigenvalue of a fundamental covariance matrix was introduced. On the basis of numerical evidence, Efron conjectured an explicit formula for this eigenvalue. This note gives a proof of that conjecture.

Key Words: Balanced experiment • Biased coin design • Covariance matrix • Maximum eigenvalue • Sequential trial.


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