Summary
Suppose that the responses to two treatments are from a single parameter exponential family. Treatments are allocated sequentially using a biased coin design (that is, the probability that the (n+1)-st subject is assigned to treatment A is a function of the proportion of the first n subjects that have been assigned to treatment A). Asymptotic error probabilities are found for a repeated significance test of the hypothesis that the two treatments elicit the same response.
References
Efron, B.: Forcing a sequential experiment to be balanced. Biometrika 58, 403–417 (1971)
Gleser, L.J.: On limiting distributions for sums of a random number of independent random vectors. Ann. Math. Stat. 40, 935–941 (1969)
Heckman, N.: Two treatment comparison with random allocation rule. Ph.D. thesis, University of Michigan, Ann Arbor, Michigan (1982)
Heckman, N.: A sequential probability ratio test using a biased coin design. Ann. Stat. 13, 789–794 (1985)
Lai, T.L., Siegmund, D.: A nonlinear renewal theory with applications to sequential analysis I. Ann. Stat. 5, 946–954 (1977)
Lalley, S.: Repeated likelihood ratio tests for curved exponential families. Z. Wahrscheinlichkeitstheor. Verw. Geb. 62, 293–321 (1983)
Wei, L.J.: The adaptive biased coin design for sequential experiments. Ann. Stat. 6, 92–100 (1978)
Woodroofe, M.B.: Nonlinear renewal theory in sequential analysis. Philadelphia: SIAM CBMS-NSF series, no. 39 (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heckman, N.E. Repeated significance tests with biased coin allocation schemes. Probab. Th. Rel. Fields 73, 627–635 (1986). https://doi.org/10.1007/BF00324857
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00324857
Keywords
- Stochastic Process
- Probability Theory
- Significance Test
- Mathematical Biology
- Error Probability