The Q-statistic is a
test statistic
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specif ...
output by either the
Box-Pierce test or, in a modified version which provides better small sample properties, by the
Ljung-Box test. It follows the
chi-squared distribution
In probability theory and statistics, the chi-squared distribution (also chi-square or \chi^2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-squa ...
. See also
Portmanteau test A portmanteau test is a type of statistical hypothesis test in which the null hypothesis is well specified, but the alternative hypothesis is more loosely specified. Tests constructed in this context can have the property of being at least moderate ...
.
The q statistic or
studentized range In statistics, the studentized range, denoted ''q'', is the difference between the largest and smallest data in a sample normalized by the sample standard deviation.
It is named after William Sealy Gosset (who wrote under the pseudonym "''Student'' ...
statistic is a statistic used for multiple significance testing across a number of means: see
Tukey–Kramer method
Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, Also occasionally as "honestly," see e.g. is a single-step multiple comparison procedure and ...
.
Statistical tests
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