These tests, also known as triangular sequential probability ratio tests, provide proper error control, unlike the truncated tests of Wald.Ĭlassic SPRT and restricted sequential tests can both be described as “fully sequential” in that data is evaluated as it gathers, and decisions to stop or proceed are made after each observation. Armitage developed so-called “restricted sequential tests” to address the need for sequential tests with a specified maximum sample size while also having rigorous error control. There seems to be no mention of the bias introduced to point estimates (maximum likelihood estimation). Regarding estimation, Wald offers just a rough sketch in terms of confidence intervals. However, these are quite crude and he offers only a limited set of upper bounds at given thresholds for type I and type II errors (p. Wald himself presents ‘truncated sequential tests’ to handle the need to stop with a definite sample size in his 1947 book “Sequential Analysis”. While there certainly were concerns regarding the duration and expenditure on any given test, these early developments could only address them to some extent.
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