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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.
balanced experiment, biased coin design, covariance matrix, maximum eigenvalue, sequential trial
Steele, J. (1980). Efron's Conjecture on Vulnerability to Bias in a Method for Balancing Sequential Trials. Biometrika, 67 (2), 503-504. http://dx.doi.org/10.1093/biomet/67.2.503
Date Posted: 27 November 2017
This document has been peer reviewed.