Steele, J. Michael2023-05-232023-05-2319802016-07-21https://repository.upenn.edu/handle/20.500.14332/42005Efron (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 experimentbiased coin designcovariance matrixmaximum eigenvaluesequential trialBiometryOther MathematicsArticle