Distributions of Sums of Squares of Rank Differences for Small Numbers of Individuals

Olds, Edwin G.

doi:10.1214/aoms/1177732332

Cited by 104 publications

(31 citation statements)

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“…For the Spearman rank correlation coefficient, the value of~d2 is computed. Then the cumulative probability for all possible~d2 up to and including the computed~d2 is determined by the Pearson Type II curve approximation described by Olds (1938Olds ( , 1949. This approximation is very accurate for moderate and large sample sizes and is much more accurate than employing Student's t for assessing the significance of the rank correlation coefficient (Zar, 1972).…”

Section: Department Of Biological Sciences Northern Illinois Universimentioning

confidence: 99%

Probabilities for Spearman rank correlation coefficients

Zar

1974

Behavior Research Methods & Instrumentation

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double phase to t = 3, whereas in the original SSA-I program t = 10, and in subsequent programs Lingoes (1973) set t = 5. We have found (on the basis of brief informal experimentation) that t =3 improves speed and efficiency at the cost of only a small number of additional double-phase iterations.Restrictions. The most meaningful restriction on APLIMDA is the response time (not the CPU time) that the user is willing to accept. Unless the IBM 360 user is in a position to use a privileged terminal (or devise a method for inducing this state), the user will often have to wait 60 sec for each iteration with a 25-order matrix on the IBM 360/65. However, since the program is interactive, the user is in a position to quickly determine (with very few iterations) the most appropriate dimensionality for the data set presently under analysis.Program Availability. Program listings of APLIMDA are available from James E. Dannemiller, Acting Director, Survey Research Office, 1914 University Avenue, The University of Hawaii, Honolulu, Hawaii 96822. With the listing (which is free of charge), we provide a trial matrix together with the correct output.

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Section: Department Of Biological Sciences Northern Illinois Universimentioning

confidence: 99%

Probabilities for Spearman rank correlation coefficients

Zar

1974

Behavior Research Methods & Instrumentation

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“…', namely (74). Each of the quantities n l,2 R and n ll2 R' is asymptotically normally distributed with zero mean and unit variance for large n. Olds [43 ] has tabulated the distribution of a quantity S related to R' by the relation R r = 1 -6S/(n 3 -n) for values of n from 2 to 10. (b) A "corner" test of association.…”

Section: Examples Of Nonparametric Statistical Tests For One Dimensiomentioning

confidence: 99%

Order statistics

Wilks¹

1948

Bull. Amer. Math. Soc.

103

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“…In this regard, the convergence to the Gaussian distribution renders its use legitimate in interpolating the p-values of r h , h = 1, 2, 3. Nonetheless, already Old (Olds, E. G., 1938) states that a distribution with a finite range causes trouble at the tails when a Gaussian fit is attempted, and, this is particularly relevant to studies where we are particularly interested in the tails. KIendall et al (KIendall, et al, 1939) add that Gaussian approximation is satisfactory for moderately large values, but for small values it is subject to the disadvantage inherent in any attempt to represent a distribution of finite range by one of infinite range, that is, the fit near the tails it is not likely to be very good.…”

Section: Introductionmentioning

confidence: 99%

A Model to Approximate the Distribution of Rank Order Associations

Tarsitano¹,

Amerise²

2017

IJSP

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The relationship between two set of ranks can be evaluated by several coefficient of rank-order association. To judge the significance of an observed value of one of these statistics we need a reliable procedure for determining the p-value of the test. In several works the t-Student has been suggested as being relevant for the description of the null distribution of many coefficients. In this article, we propose a new model of density function, the generalized Gaussian on a finite range, which can be used to model data exhibiting a symmetrical unimodal density with a bounded domain. Several simulations illustrate the advantages of this technique over conventional methods. This is particularly useful in the case the number of ranks is larger than the threshold for which the exact null distribution is known, but lower than the threshold for which the asymptotic Gaussian approximation becomes valid.

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Distributions of Sums of Squares of Rank Differences for Small Numbers of Individuals

Cited by 104 publications

References 0 publications

Probabilities for Spearman rank correlation coefficients

Probabilities for Spearman rank correlation coefficients

Order statistics

A Model to Approximate the Distribution of Rank Order Associations

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