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Inferential statistics

2 articles
SamplingPoint estimationConfidence intervalHypothesis testingP valueType i and ii errorsMaximum likelihoodStatistical inferenceFrequentist inferenceStatistical hypothesis testStatistical hypothesis testingNull hypothesisAlternative hypothesisSignificance levelType i and type ii errorsStatistical powerPower statisticsCredible intervalPrediction intervalTolerance intervalInterval estimationLikelihood intervalPivotal quantityOne and two tailed tests+ 101 de plus
Probability & StatisticsLicenceExplication10 min

Three Points from a Thousand People, and the Two Roundings That Cancel

The 95 percent margin on a proportion is almost exactly 1 over the square root of the sample size, because p(1-p) is flat enough near its peak to call a quarter and 1.96 is close enough to 2, and those two roundings are reciprocal so they annihilate. At N = 1000 the shortcut gives 3.16 percent against an exact 3.04, and it always errs on the conservative side. Reporting one standard error instead, 1.55 percent, describes a 68 percent interval rather than a 95 percent one.

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Probability & StatisticsLicenceAnalyse9 min

Five Numbers, Two Answers, and the Divisor Nobody Asks About

The standard deviation of 1, 2, 3, 4, 5 is either 1.4142 or 1.5811, and offering one of them without asking which question you are answering is the only wrong move. The sum of squared deviations is 10 either way, so everything turns on whether you divide it by 5 or by 4. Bessel's correction makes the variance unbiased and leaves the standard deviation biased low by about six percent at this sample size, and a third divisor beats both of them if you optimise for mean squared error instead.

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