Statistics · Hypothesis testing
Chapter 1 · 3
The idea
Hypothesis tests for the Poisson distribution
Testing a claim about a mean rate λ: hypotheses written in λ, the Poisson tail as the measure of surprise, rescaling λ to the interval actually observed, one- and two-tailed critical regions with their actual significance levels, why a count of zero sometimes can never be significant, and tests that use a Poisson approximation to a binomial.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Statistics · Hypothesis testing
Hypothesis tests for the Poisson distribution
Testing a claim about a mean rate λ: hypotheses written in λ, the Poisson tail as the measure of surprise, rescaling λ to the interval actually observed, one- and two-tailed critical regions with their actual significance levels, why a count of zero sometimes can never be significant, and tests that use a Poisson approximation to a binomial.
Why it works
A busy ten seconds, or a radioactive pebble?
A Geiger counter in a school laboratory picks up background radiation. It clicks at random, at a mean rate of every seconds. Mia holds a granite pebble next to it and counts clicks in seconds. Is the pebble radioactive, or was that just a busy ten seconds?A Poisson count has no number of trials, so there is no proportion to test. The parameter is the mean rate , and both hypotheses are written in it:
Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
Start freeTakes a minute — no card.