Test Statistic

A quantity computed from the data (e.g. t, z, F, χ²) from which the p-value of the test is derived.

Also known as: test statistic, test quantity

A test statistic is the bridge between data and decision: it condenses the observations into a single number whose distribution under H₀ is known. From this distribution the p-value is obtained as the probability of seeing at least this value under H₀.

t statistic — one-/two-sample t-test: $t = (\overset{x}{ˉ} - μ_{0}) / (s / n)$
z statistic — with known σ or large n
F statistic — ANOVA and variance comparisons: ratio of two variance estimators
χ² statistic — distribution comparisons, frequency tables, variance tests

Used in

Hypothesis Test

In the Algorithm Lab

hypothesis/one-sample-t-test
hypothesis/two-sample-t-test
hypothesis/f-test
hypothesis/chi-square-variance

Sources

Fisher, R. A. — Statistical Methods for Research Workers, 1925
Neyman, J. & Pearson, E. S. — On the Problem of the Most Efficient Tests, 1933

Test Statistic

See also

Used in

In the Algorithm Lab

Sources