Showing papers on "Wilcoxon signed-rank test published in 1976"

A two-sample Anderson-Darling rank statistic

Abstract: SUMMARY A two-sample Anderson-Darling statistic is introduced and small-sample percentage points are given. An approximation to the distribution is also given. The statistic is related to Wilcoxon's and Mood's rank statistics. Asymptotic power comparisons are made with other two-sample rank statistics for shifts in location and scale.

Introductory medical statistics

Abstract: Data presentation Describing cuves and distributions The normal distribution curve Introduction to sampling, errors and accuracy Introduction to probability Binomial probabilities Poisson probabilities Introduction to statistical significance The chi-squared test The Fisher exact probability test The t-test Difference between proportions for independent and for non-independent (McNemar's test for paired proportions) samples Wilcoxon, Mann-Whitney and sign tests Survival rate calculations The logrank and Mantel-Haenszel tests Regression and correlation Analysis of variance Multivariate analysis: the Cox proportional hazards model Sensitivity and specificity Clinical trials Cancer treatment success, cure and quality of life Risk specification with emphasis on ionising radiation Types of epidemiological study: case-control, cohort and cross-sectional Glossary of rates and ratios: terminology in vital statistics References Index

A class of location-scale nonparametric tests

Abstract: SUMMARY A class of two-sample nonparametric tests for location and scale shift, simultaneously, is proposed. The asymptotic distribution of the proposed class is obtained both under the hypothesis and alternative. Using this result it is shown how the asymptotic relative efficiency of tests in the proposed class can be obtained. F2(x) = F(a2x +4f2), respectively. The purpose of this paper is to study a class of two-sample nonparametric test statistics which can be used to test HO: Fl(x) = F2(x) = F(x) for all real x, versus the alternative Ha:acc * a2 or /h t /h' or both. The proposed statistics will be expressed as functions of two nonparametric statistics, one sensitive to scale shift and the other to location shift. Lepage (1971) proposed a statistic which is a combination of the Wilcoxon and Ansari- Bradley statistics. Furthermore, he showed that since the Wilcoxon and Ansari-Bradley statistics are uncorrelated under Ho, his proposed statistic has a limiting central chi- squared distribution with two degrees of freedom. Thus the critical values needed to carry out an approximate test of Ho can be obtained from a standard chi-squared table. The question regarding the asymptotic power behaviour of Lepage's statistic is of interest but is not, however, discussed by Lepage. Thus the asymptotic relative efficiency of the proposed statistics will also be discussed, as a means of comparing such statistics.

Two-Stage Wilcoxon Tests of Hypotheses

Abstract: Two-stage Wilcoxon signed ranks tests and Wilcoxon-Mann-Whitney tests are presented for general one-sided alternatives. A probability recurrence relation is given for the two-stage signed ranks statistics under the null hypothesis. For each test the limiting bivariate distribution of the standardized statistics is normal. With certain restrictions on the sample sizes, the null limiting distributions are both the one considered by Owen [8], so large sample tests can be formed using existing tables. Monte Carlo results suggest that these tests can considerably reduce the expected number of observations without reducing power relative to the usual one-stage tests.

An approximation to the exact distribution of the wilcoxon-mann-whitney rank sum test statistic

Abstract: An approximation to the exact distribution of the Wilcoxon rank sum test (Mann-Whitney U-test) and the Siegel-Tukey test based on a linear combination of the two-sample t-test applied to ranks and the normal approximation is compared with the usual normal approximation. The normal approximation results in a conservative test in the tails while the linear combination of the test statistics provides a test that has a very high percentage of agreement with tables of the exact distribution. Sample sizes 3≤m, n≤50 were considered.

The Benard-Van Elteren statistic and nonparametric computation

Abstract: A general computer program which generates either the Wilcoxon, Kruskal-Wallis, Friedman, or extended Friedman statistic (where the numbers of cell observations nij may be any positive integer or zero) can be formulated simply by using the computational algorithm for the Benard-Van Elteren statistic. It is shown that the Benard-Van Elteren statistic can be computed using matrix algebra subroutines including multiplication and inverse or g-inverse computational algorithms in the case where the rank of the matrix V of the variances and covariances of the column totals is k-1. For the case where the rank of V is less than k-1 the use of the g-inverse is shown to greatly reduce the labors of calculation. In addition, the use of the Benard-Van Elteren statistic in testing against ordered alternatives is indicated.

Some distribution-free rane-like statistics having the mann-whitney-wilcoxon null distribution

Abstract: In this note we suggest a class of two-sample test statistics iich have, as their null distribution,the Mann-Whitney-Wilcoxon ill distribution. An interesting property of these statistics is lat many are not rank statistics; that is, they cannot be coumplited from, the ranks of the original observations. However, they %e still distribution-free when the two populations are identi-il. This class contains the Mann-Whitney-Wilcoxon test for the niality of location parameters of two distributions and a two-aiaple test for equality of spreads of two distributions recently ivestigated by Fligner and Killeen (1976)

Asymptotic Linearity of Wilcoxon Signed-Rank Statistics

Abstract: As a "robust" alternative to the least squares estimates for a regression parameter, Koul (1969) proposed new estimates based on signed-rank statistics. To find out their asymptotic distribution Koul proved that under quite general assumptions, the signed-rank statistics of Wilcoxon type are asymptotically linear in the sense that they are uniformly approximable by linear forms in the regression parameter. More general results have been obtained by Van Eeden (1972) in a paper which is an analog to Jureckova's paper (1969) dealing with linear rank statistics. In 1972 the author proved that the statistic used to define the Hodges-Lehmann estimate for a location parameter is asymptotically linear in a stronger sense, the result being to Koul's theorem what the central limit theorem is to the weak law of large numbers. For the general linear regression model with one parameter the signed-rank statistics are proved to be linear in a strong sense, that is, the differences between the statistics and the linear forms mentioned above, properly normalized, converge weakly to linear processes. Results in this direction for linear rank statistics have been obtained by Jureckova (1973). As an application of the theorems presented here, one can construct new estimates for the squared $L_2$-norm of the underlying density, and this in much the same way as in Antille (1974). It is also possible to get more information about the asymptotic behavior of the linearized versions, proposed by Kraft and Van Eeden (1972).

An extended class of matched pairs tests based on powers of ranks

Abstract: A large class of rank tests, which includes the familiar sign test and the Wilcoxon signed-ranks test, is described and discussed. This class of distribution-free tests provides a flexible basis for testing research hypotheses of various forms. Exact small sample and approximate large sample procedures are considered. Applications of these procedures are presented, including simple numerical examples.

Nonparametric and Distribution-Free Methods

Abstract: This chapter discusses nonparametric and distribution-free methods. The main advantage of nonparametric and distribution-free statistical tests is that they do not require the population(s) being sampled to be normally distributed, and therefore, are applicable when gross nonnormality is suspected. The primary disadvantage of these methods is that when normality does exist, they are less powerful than the corresponding parametric tests. The power efficiency of a nonparametric or distribution-free test is almost always less than 100%, and sometimes much less. Thus it is wasteful to use these methods when parametric tests are applicable. The rank-sum test finds out the difference between the locations of tw o independent samples. The Kruskal-Wallis H test figures out differences among the locations of two or more independent samples. The Wilcoxon test finds out the difference between the locations of two matched samples. The median and sign tests are used primarily to obtain a quick approximation of the results of more powerful tests when samples are large. The median test is used to compare the locations of two or more independent samples. The sign test is used to compare the locations of two or more matched samples.

The Absolute Normal Scores Test for Symmetry.

Abstract: The absolute normal scores test (K) is described as a test for the symmetry of a distribution of scores about a location parameter designated as 0. The test is compared to the sign test (S) and the Wilcoxon test (W) as an alternative to the t-test. Power comparisons are made among the K, S, W, and t tests. An example is presented where the sample size is less than 20. The large sample approximation to the normal distribution is also illustrated.