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standard deviation contributes additional uncertainty into the values calculated. This complicates the problem of finding the probability distribution of any statistic that is
348:{\displaystyle q_{n,\nu }={\frac {\max\{\,x_{1},\ \dots ,\ x_{n}\,\}-\min\{\,x_{1},\ \dots ,\ x_{n}\}}{s}}=\max _{i,j=1,\dots ,n}\left\{{\frac {x_{i}-x_{j}}{s}}\right\}}
610:
Newman D. (1939). "The
Distribution of Range in Samples from a Normal Population Expressed in Terms of an Independent Estimate of Standard Deviation".
529:
standard deviation, and thus something that differs from one random sample to the next, is essential to the definition and the distribution of the
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of the distribution from which the sample is drawn, and therefore its probability distribution is the same regardless of those parameters.
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47:"), and was introduced by him in 1927. The concept was later discussed by Newman (1939), Keuls (1952), and
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Douglas C. Montgomery (2013) "Design and
Analysis of Experiments", eighth edition, Wiley, page 98.
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Keuls M. (1952). "The Use of the "Studentized Range" in
Connection with an Analysis of Variance".
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John Neter, Michael H. Kutner, Christopher J. Nachtsheim, William
Wasserman (1996)
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John A. Rafter (2002). "Multiple
Comparison Methods for Means".
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means that the variable's scale was adjusted by dividing by an
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in some unpublished notes. Its statistical distribution is the
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113:(0, 1) distribution of numbers, and another random variable
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69:, and the Duncan's step down procedure, and establishing
807:, second edition, Duxbury Press, pages 451–452.
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373:are typically the means of samples each of size
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575:Student (1927). "Errors of routine analysis".
61:procedures, such as the single step procedure
521:). The fact that the standard deviation is a
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358:has the Studentized range distribution for
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366:degrees of freedom. In applications, the
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421:(the number of observations or groups)
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411:(the probability of rejecting a true
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782:Pearson, E.S.; Hartley, H.O. (1970)
525:standard deviation rather than the
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738:it lacks sufficient corresponding
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798:Applied Linear Statistical Models
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43:(who wrote under the pseudonym "
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136:degrees of freedom. Then
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753:more precise citations.
481:does not depend on the
400:The critical value of
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71:confidence intervals
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67:Newman–Keuls method
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651:10.1007/bf01908269
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