الاسم
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الصيغة
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الافتراضات أو الملاحظات
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One-sample z-test
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(Normal population or n > 30) and σ known.
(z is the distance from the mean in relation to the standard deviation of the mean). 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).
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Two-sample z-test
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Normal population and independent observations and σ1 and σ2 are known
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Two-sample pooled t-test, equal variances*
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[1]
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(Normal populations or n1 + n2 > 40) and independent observations and σ1 = σ2 and σ1 and σ2 unknown
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Two-sample unpooled t-test, unequal variances*
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[1]
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(Normal populations or n1 + n2 > 40) and independent observations and σ1 ≠ σ2 and σ1 and σ2 unknown
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One-proportion z-test
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n .p0 > 10 and n (1 − p0) > 10 and it is a SRS (Simple Random Sample), see notes.
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Two-proportion z-test, pooled for
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n1 p1 > 5 and n1(1 − p1) > 5 and n2 p2 > 5 and n2(1 − p2) > 5 and independent observations, see notes.
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Two-proportion z-test, unpooled for
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n1 p1 > 5 and n1(1 − p1) > 5 and n2 p2 > 5 and n2(1 − p2) > 5 and independent observations, see notes.
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One-sample chi-square test
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One of the following
• All expected counts are at least 5
• All expected counts are > 1 and no more than 20% of expected counts are less than 5
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*Two-sample F test for equality of variances
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Arrange so > and reject H0 for [2]
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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. ... Definitions of other 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
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= 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
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= x/n = sample proportion, unless specified otherwise
= hypothesized population proportion
= proportion 1
= proportion 2
= hypothesized difference in proportion
= minimum of n1 and n2


= Chi-squared statistic
= F statistic
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