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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 H1H_1 false (H0H_0 true) H1H_1 true (H0H_0 false)
H1H_1 rejected True Negative False Negative (Type 2)
(H0H_0 accepted) P=1α\mathop{P}= 1-\alpha P=β\mathop{P}= \beta
H1H_1 accepted False Positive (Type 1) True Positive
(H0H_0 rejected) P=α\mathop{P}= \alpha P=1β\mathop{P}= 1-\beta

pp 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.