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  2. Studentized range - Wikipedia

    en.wikipedia.org/wiki/Studentized_range

    has the Studentized range distribution for n groups and ν degrees of freedom. In applications, the x i are typically the means of samples each of size m, s 2 is the pooled variance, and the degrees of freedom are ν = n(m − 1). The critical value of q is based on three factors: α (the probability of rejecting a true null hypothesis)

  3. Studentized range distribution - Wikipedia

    en.wikipedia.org/wiki/Studentized_range_distribution

    The studentized range distribution function arises from re-scaling the sample range R by the sample standard deviation s, since the studentized range is customarily tabulated in units of standard deviations, with the variable q = R ⁄ s. The derivation begins with a perfectly general form of the distribution function of the sample range, which ...

  4. Tukey's range test - Wikipedia

    en.wikipedia.org/wiki/Tukey's_range_test

    The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.

  5. Q-statistic - Wikipedia

    en.wikipedia.org/wiki/Q-statistic

    The Q-statistic or q-statistic is a test statistic: The Box-Pierce test outputs a Q-statistic (uppercase) ... which follows the studentized range distribution

  6. Dixon's Q test - Wikipedia

    en.wikipedia.org/wiki/Dixon's_Q_test

    However, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [ 1 ] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.

  7. Duncan's new multiple range test - Wikipedia

    en.wikipedia.org/wiki/Duncan's_new_multiple_range...

    Duncan's multiple range test makes use of the studentized range distribution in order to determine critical values for comparisons between means. Note that different comparisons between means may differ by their significance levels- since the significance level is subject to the size of the subset of means in question.

  8. Q distribution - Wikipedia

    en.wikipedia.org/wiki/Q_distribution

    In mathematics and statistics, Q-distribution or q-distribution may refer to: Q-function, the tail distribution function of the standard normal distribution; The studentized range distribution, which is the distribution followed by the q-statistic (lowercase Q; the Q-statistic with uppercase Q, from the Box-Pierce test or Ljung-Box test, follows the chi-squared distribution)

  9. Studentization - Wikipedia

    en.wikipedia.org/wiki/Studentization

    In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the adjustment consisting of division of a first-degree statistic derived from a sample, by a sample-based estimate of a population standard deviation.