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共通統計量

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See legend defining symbols at bottom of table. The statistics for some other tests have their own articles, including the Wald test and the likelihood ratio test.

統計量 公式 Assumptions or notes
z-検定 (正規母集団 or n > 30) and σが既知.

(z is the distance from the mean in relation to 平均からの標準偏差). For non-normal distributions it is possible to calculate a minimum proportion of a population that falls within k standard deviations for any k (see: Chebyshev's inequality).

t-検定

(Normal population or n > 30) and σ unknown
One-sample chi-square test One of the following

• All expected counts are at least 5

• All expected counts are > 1 and no more that 20% of expected counts are less than 5

*Two-sample F test for equality of variances Arrange so > and reject H0 for [1]
Definition of symbols , the probability of Type I error (rejecting a null hypothesis when it is in fact true)

= sample size
= sample 1 size
= sample 2 size
= sample mean
= hypothesized population mean
= population 1 mean
= population 2 mean
= population standard deviation
= population variance
= sample standard deviation
= sample variance
= sample 1 standard deviation
= sample 2 standard deviation
= t statistic
= degrees of freedom
= sample mean of differences
= hypothesized population mean difference
= standard deviation of differences
= x/n = sample proportion, unless specified otherwise
= hypothesized population proportion
= proportion 1
= proportion 2
= minimum of n1 and n2


= Chi-squared statistic
= F statistic

In general, the subscript 0 indicates a value taken from the null hypothesis, H0, which should be used as much as possible in constructing its test statistic.
  1. ^ NIST handbook: F-Test for Equality of Two Standard Deviations (should say "Variances")