Metrika

, Volume 49, Issue 1, pp 41-52

A sequential procedure to test three values of a binomial parameter

  • Mark E. PaytonAffiliated withDepartment of Statistics, Oklahoma State University, Math Science Bldg. Room 301, Stillwater, OK 74078-1056, USA (e-mail: mpayton@okway.okstate.edu)
  • , Linda J. YoungAffiliated withDepartment of Biometry, University of Nebraska-Lincoln, 103 Miller Hall, East Campus, Lincoln, NE 68583-0712, USA (e-mail: ljyoung1@unl.edu)

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Abstract.

Sequential tests to decide among three binomial probabilities are needed in many situations, such as acceptance sampling used to determine the proportion of defective items and presence and absence sampling to decide whether pest species are causing economic damage to a crop such as corn. Approximate error probabilities associated with Armitage's (1950, JRSS B) method of simultaneously conducting three sequential probability ratio tests (SPRTs) are derived for the binomial distribution. These approximations provide a basis for adjusting the error rates used to establish the individual SPRTs so that the desired overall error rates are attained. Monte Carlo simulation is used to evaluate the revised procedure.

Key words: Sequential Probability Ratio Test Bernoulli trials sequential sampling hypothesis testing