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  "body": "\n## Summary\n\nConsider a family of densities indexed by a real parameter.\nIt has a monotone likelihood ratio in a statistic $T$ when larger parameters make larger values of $T$ relatively more likely.\nThe ratio of the densities at two parameter values is then a nondecreasing function of $T$.\nThis property makes one-sided testing simple: tests that reject for large $T$ are optimal.\nOne-parameter exponential families with an increasing natural parameter have this property.\n\n## Explanations\n\n### L1 human\n\nThink of $T$ as a signal that points towards larger parameter values.\nIn a family with a monotone likelihood ratio, the larger $T$ is, the more the data favour a larger parameter over a smaller one, for every pair of parameters.\nFor coin tosses with head probability $p$, the number of heads $T$ is such a signal.\nSeeing more heads always favours a larger $p$ over a smaller one.\n",
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