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  "body": "\n## Summary\n\nThe sequential probability ratio test, or SPRT, is a sequential test of a simple null hypothesis against a simple alternative.\nAfter each observation it updates the likelihood ratio of the data and stops as soon as this ratio leaves a fixed interval.\nAbraham Wald introduced it, and it is the basic procedure of [[sequential analysis|9CWYNB9003]].\nAmong all tests with the same error probabilities, it needs the smallest expected number of observations under both hypotheses.\n\n## Explanations\n\n### L1 human\n\nTwo explanations of the data compete, and each new observation makes one of them a little more plausible than the other.\nThe test keeps a running score, the ratio of how likely the data are under the two explanations.\nIt stops and picks the alternative when the score climbs above an upper bar, and picks the null hypothesis when it falls below a lower bar.\nFor example, to test whether a coin shows heads with probability $1/2$ or $2/3$, each head multiplies the score by $4/3$ and each tail by $2/3$.\n",
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