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A statistical hypothesis test is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets.

Parameters and Terms

Decision ╲ Reality $H_1$ false ($H_0$ true) $H_1$ true ($H_0$ false)
$H_1$ rejected True Negative False Negative (Type 2)
($H_0$ accepted) ${\mathrm{P}}= 1-\alpha$ ${\mathrm{P}}= \beta$
$H_1$ accepted False Positive (Type 1) True Positive
($H_0$ rejected) ${\mathrm{P}}= \alpha$ ${\mathrm{P}}= 1-\beta$

$p$ is the probability that a given result would occur if the null hypothesis is true.

Power of a test (1 − β)

Mean Tests

Tests whether the means of independent sample sets are significantly different.