Statistics & Probability

Two-proportion z-test for conversion experiments — p-value, confidence, relative lift and whether it's significant.

Required visitors per variant to detect a target lift at your power and significance — before you launch.

Wald and Wilson confidence intervals for a proportion — the honest error bars around your conversion rate.

nPr, nCr and n! for counting arrangements and selections — the foundation of combinatorics and probability.

Update a prior probability with new evidence — the engine of rational belief, spam filters and medical reasoning.

Convert a value to a z-score and percentile, or find probabilities under the bell curve — for any mean and SD.

Probability of exactly k events when events occur at a known average rate — arrivals, defects, calls, hits.

Test whether two categorical variables are associated — independence test for 2×2 contingency tables.

How simulation accuracy improves with sample count — standard error, and samples needed for a target precision.

Probability that two people in a group share a birthday — the classic counter-intuitive probability result.

Expected value, variance and standard deviation of a discrete distribution — the foundation of decision theory.