Abstract Two procedures are suggested for testing the hypothesis of randomness against alternatives of a linear trend and a cyclical trend, respectively. Both procedures reduce to tests of the hypothesis that the parameter of a binomial distribution is p 0 against the alternative that it is p 1 and can, therefore, be easily sequentialized. The expected number of observations required by the sequential test against linear trend is smaller than the corresponding number of observations of other tests in current use. * This research was supported by the United States Air Force under Contract AF 18(600)-778, monitored by the Office of Scientific Research, Air Research and Development Command. A more theoretical discussion of the two tests—as well as others—is given in the author's report to the Office of Scientific Research, “Sequential Tests of Randomness,” dated December, 1953.
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