SPRT

The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald.Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of thumb for when all the data is collected (and its likelihood ratio known).

While originally developed for use in quality control studies in the realm of manufacturing, SPRT has been formulated for use in the computerized testing of human examinees as a termination criterion.

As in classical hypothesis testing, SPRT starts with a pair of hypotheses, say ${\displaystyle H_{0}}$ and ${\displaystyle H_{1}}$ for the null hypothesis and alternative hypothesis respectively. They must be specified as follows:

The next step is calculate the cumulative sum of the log-likelihood ratio, ${\displaystyle \log \Lambda _{i}}$, as new data arrive: with ${\displaystyle S_{0}=0}$, then, for i=1,2,...,

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