P-value Calculator

Significance from a z-score.

Sample design decides whether a result can be trusted as much as the arithmetic does: a random sample of a thousand people can describe a country, while a large voluntary response sample describes only itself. Effect size and confidence interval together say more than a p-value alone.

Statistics in American teaching and research is organised around the normal curve: standard deviation measures spread, a z-score expresses a value in units of it, and a p-value below 0.05 is the conventional line for calling a result significant. Confidence intervals widen quickly as samples shrink, and a result is only as good as the sample it came from.

The 0.05 threshold is a convention, not a law of nature: it means a result this extreme would arise by chance about one time in twenty if there were no real effect.

Sampling error and bias are different problems: a larger sample shrinks the first and does nothing about the second. A confidence interval describes the range the true value plausibly occupies, not the spread of the data.

P-value Calculator sits with the rest of the library's maths work, and it rests on the same statistical arithmetic the way a textbook or an exam paper does. Its answer is only as good as the assumptions standing behind it. The quantities it works from — z-score — are the ones a real statistical question actually turns on, and each carries a convention of its own, set out below.

Mathematics is the one subject here that depends on nothing local: the same theorem holds in Ohio and Osaka, and the same fraction carries the same value everywhere. What changes is how results are written — American schooling teaches decimal notation and long division, and business arithmetic runs on fractions of a dollar.

Precision and rounding are where most practical errors creep in.