Tagged “confidence-intervals”

2 articles.

14 September 20264 min readStatistical Inference

The 95% Interval That Covers 81% of the Time

The textbook confidence interval for a proportion has exact coverage you can compute by summing over the n+1 possible samples, and at n = 30 with p = 0.10 it is 0.8085 rather than 0.95. Coverage does not improve monotonically with n, and in a rare-event setting it can fall to 0.0392. Two one-line alternatives fix it.

Statistics

10 September 202610 min readStatistical Inference

What a Sample Can and Cannot Tell You

Estimators as random variables with distributions of their own, the case where the unbiased estimator is the worse one, what a confidence interval actually promises and the standard interval that delivers 87% where it advertises 95%, and what a p-value is a probability of - every figure computed exactly or by fixed-seed simulation.

StatisticsProbability