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  "body": "\n## Summary\n\nThe score test is a [[hypothesis test|087P03NEND]] that uses the slope of the log-likelihood at the null value of the parameter.\nIf the null hypothesis is true, the [[score|CP97GRVTQ0]] there should be close to zero, measured against the [[Fisher information|G1Z3WSTE8Q]].\nIt needs only the fit under the null hypothesis, and it is also called Rao's score test or the Lagrange multiplier test.\n\n## Explanations\n\n### L1 human\n\nAt the true parameter, the log-likelihood is flat on average: it has no tendency to go up or down.\nThe score test checks whether the log-likelihood is steep at the value claimed by the null hypothesis.\nA steep slope means that moving away from that value would raise the likelihood of the data by a large amount.\nFor a coin with $60$ heads in $100$ tosses and $H_0 \\colon p = 0.5$, the score statistic is $(60 - 50)^2/25 = 4$, which is beyond the $95\\%$ chi-squared quantile $3.84$.\n",
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