RANK CORRELATION BETWEEN TWO VARIABLES, ONE OF WHICH IS RANKED, THE OTHER DICHOTOMOUS
56
Citation
4
Reference
10
Related Paper
Citation Trend
Abstract:
Rank correlation is one of the most useful statistical techniques available for the treatment of data arising in experimental and applied psychological research. Chambers (1946) has indicated the type of data most frequently occurring in these fields, and has pointed out the advantages of Kendall's r over Spearman's p or any form of transformation to ordinal form. Given the use of T when tied rankings are present (Kendall, 1946) it seemed possible to extend the method to cover a very common problem in psychology, namely, determination of the relation between two variables, one of which is expressed as a ranking and the other as a dichotomy. In applied or field work the relation of a psychological 'measurement' and an external criterion nearly always appears in this form. The usual method of determining the relationship consists of reducing the ranking to a dichotomy and calculating x2 for the 2 x 2 table which results. That this may lead to inaccuracy can be seen from the following example:Keywords:
Rank correlation
Rank (graph theory)
Abstract In this paper, several characterizations are given of the group of eigenvalues of a rank one transformation. One of these is intimately related to the corresponding expression for the maximal spectral type of a rank one transformation given in an earlier paper.
Rank (graph theory)
Transformation group
Cite
Citations (10)
The purpose of this paper is to present the relationship between nonparametric and parametric analysis by means of rank transformation. It is shown that in case of large sample, the resulting statistics getting from Wilcoxon rank test, Kruskal-Wallis and Friedman rank test are equivalent to the ratio of the sum of squares for treatment divided by mean square for the total variability calculated by ranks in the manner of the analysis of variance. It is also suggested that this method can be extended to factorial design experiments, and a detail procedure is given.
Rank (graph theory)
Friedman test
Rank correlation
Cite
Citations (0)
Rank (graph theory)
Constant (computer programming)
Zero (linguistics)
Cite
Citations (16)
Rank (graph theory)
Cite
Citations (0)
In this paper, we consider an m x n regular matrix A over a commutative ring A (-a matrix whose range is direct summand of A m ) and a necessary and sufficient condition in terms of determinantal rank is obtained for solvability of Ax = b. In the light of this result we define rank-function for matrices.
Rank (graph theory)
Matrix (chemical analysis)
Augmented matrix
Cite
Citations (3)
This paper proposes a generalized and structured method for use for rank determination in rankorder statistics.The sampled populations may be measurements on as low as the ordinal scale and need not be continuous or numeric.The proposed method would readily enable the researcher assign ranks to sample observations without the need to first arrange the observations in some form as is often the case with the traditional approach in the ranking of observations.The method also provides expressions that are intrinsically and structurally formulated to enable one easily break ties and assign appropriate ranks to any tied observations if need be in a straight forward manner.The proposed method is illustrated with some sample data and shown to be often easier to use in practice than the traditional method and of more generalized and wider applicability than some other existing formulations which are often limited in their use.
Rank (graph theory)
Cite
Citations (0)
The problem of n judges ranking r objects is considered in the situation where ties are permitted. Asymtotic distributions under the null hypothesis of complete randomness in the rankings are derived for the test statistics of average rank correlations between all pairs of ranking where the rank correlations are measured either by Spearman rho or Kendall tau. The relative efficeincies of these average rank correlatins are derived using approximate Bahadur slope and limiting pitman efficiency, and in both cases the Kendall statistic is shown to be more efficient. Some interpretatins of these and related results are also given.
Rank correlation
Statistic
Rank (graph theory)
Limiting
Cite
Citations (5)
Abstract Let $R$ be a smooth affine domain of dimension $d\geq 3$ over $\overline{{\mathbb{F}}}_p$ with $p\neq 2$. Let $P$ be a projective $R$-module of rank $d-1$ with trivial determinant. We prove that $P$ splits off a free summand of rank 1 if and only if $P$ surjects onto a complete intersection ideal of height $d-1$.
Rank (graph theory)
Complete intersection
Cite
Citations (2)
We show that there is a bound depending only on g, r and [ K : \mathbb Q ] for the number of K -rational points on a hyperelliptic curve C of genus g over a number field K such that the Mordell–Weil rank r of its Jacobian is at most g–3 . If K = \mathbb Q , an explicit bound is 8rg + 33(g–1) + 1 . The proof is based on Chabauty’s method; the new ingredient is an estimate for the number of zeros of an abelian logarithm on a p -adic ‘annulus’ on the curve, which generalizes the standard bound on disks. The key observation is that for a p -adic field k , the set of k -points on C can be covered by a collection of disks and annuli whose number is bounded in terms of g (and k ). We also show, strengthening a recent result by Poonen and the author, that the lower density of hyperelliptic curves of odd degree over \mathbb Q whose only rational point is the point at infinity tends to 1 uniformly over families defined by congruence conditions, as the genus g tends to infinity.
Rank (graph theory)
Hyperelliptic curve
Hyperelliptic curve cryptography
Rational point
Cite
Citations (33)
Rank correlation is one of the most useful statistical techniques available for the treatment of data arising in experimental and applied psychological research. Chambers (1946) has indicated the type of data most frequently occurring in these fields, and has pointed out the advantages of Kendall's r over Spearman's p or any form of transformation to ordinal form. Given the use of T when tied rankings are present (Kendall, 1946) it seemed possible to extend the method to cover a very common problem in psychology, namely, determination of the relation between two variables, one of which is expressed as a ranking and the other as a dichotomy. In applied or field work the relation of a psychological 'measurement' and an external criterion nearly always appears in this form. The usual method of determining the relationship consists of reducing the ranking to a dichotomy and calculating x2 for the 2 x 2 table which results. That this may lead to inaccuracy can be seen from the following example:
Rank correlation
Rank (graph theory)
Cite
Citations (56)