An extended class of permutation techniques for matched pairs

A class of matched-pairs permutation techniques based on distances between each pair of observed signed values is considered. Although many commonly-used inference techniques for matched pairs are members of this class, some of the more appealing inference techniques among this class have received very little attention. Two new simple rank tests of this class jointly possess both intuitive properties and location-alternative power characteristics which appear more appealing than the corresponding characteristics of either the sign test or the Wllcoxon signed-ranks test. In particular, power comparisons based on slmula-tions indicate that these new rank tests are jointly as good or even vastly superior to the sign test or the Wilcoxon signed-ranks test for location alternatives involving five symmetric distributions. The five distributions selected for these com-parisons include the Laplace, logistic, normal, uniform and a U-shaped distribution     

Computation of finite population parameters and approximate probability values for multi-response randomized block permutation procedures (mrbp)

An algorithm is presented for computing the finite population parameters and the approximate probability values associated with a recently-developed class of statistical inference techniques termed multi-response randomized block permutation procedures (MRBP).     

An exact two-sample test based on the baumgartner-weiss-schindler statistic and a modification of lepage's test

It is shown that the nonparametric two-saniDle test recently proposed by Baumgartner, WeiB, Schindler (1998, Biometrics, 54, 1129-1135) does not control the type I error rate in case of small sample sizes. We investigate the exact permutation test based on their statistic and demonstrate that this test is almost not conservative. Comparing exact tests, the procedure based on the new statistic has a less conservative size and is, according to simulation results, more powerful than the often employed Wilcoxon test. Furthermore, the new test is also powerful with regard to less restrictive settings than the location-shift model. For example, the test can detect location-scale alternatives. Therefore, we use the test to create a powerful modification of the nonparametric location-scale test according to Lepage (1971, Biometrika, 58, 213-217). Selected critical values for the proposed tests are given.     

Computation of exact probability values for multi-response permutation procedures (MRPP)

An algorithm is presented for computing the exact probability value associated with a recently–developed class of statistical inference techniques termed multi–response permutation procedures (MRPP).     

Modified mantel-haenszel procedures for matched pairs

In the prospective study of a finely stratified population, one individual from each stratum is chosen at random for the “treatment” group and one for the “non-treatment” group. For each individual the probability of failure is a logistic function of parameters designating the stratum, the treatment and a covariate. Uniformly most powerful unbiased tests for the treatment effect are given. These tests are generally cumbersome but, if the covariate is dichotomous, the tests and confidence intervals are simple. Readily usable (but non-optimal) tests are also proposed for poly-tomous covariates and factorial designs. These are then adapted to retrospective studies (in which one “success” and one “failure” per stratum are sampled). Tests for retrospective studies with a continuous “treatment” score are also proposed.     

A permutation test for multivariate data with grouped components

In this paper, we consider a nonparametric test procedure for multivariate data with grouped components under the two sample problem setting. For the construction of the test statistic, we use linear rank statistics which were derived by applying the likelihood ratio principle for each component. For the null distribution of the test statistic, we apply the permutation principle for small or moderate sample sizes and derive the limiting distribution for the large sample case. Also we illustrate our test procedure with an example and compare with other procedures through simulation study. Finally, we discuss some additional interesting features as concluding remarks.     

A comparison of several adaptive tests for paired data

In the last few years, two adaptive tests for paired data have been proposed. One test proposed by Freidlin et al. [On the use of the Shapiro–Wilk test in two-stage adaptive inference for paired data from moderate to very heavy tailed distributions, Biom. J. 45 (2003), pp. 887–900] is a two-stage procedure that uses a selection statistic to determine which of three rank scores to use in the computation of the test statistic. Another statistic, proposed by O'Gorman [Applied Adaptive Statistical Methods: Tests of Significance and Confidence Intervals, Society for Industrial and Applied Mathematics, Philadelphia, 2004], uses a weighted t-test with the weights determined by the data. These two methods, and an earlier rank-based adaptive test proposed by Randles and Hogg [Adaptive Distribution-free Tests, Commun. Stat. 2 (1973), pp. 337–356], are compared with the t-test and to Wilcoxon's signed-rank test. For sample sizes between 15 and 50, the results show that the adaptive test proposed by Freidlin et al. and the adaptive test proposed by O'Gorman have higher power than the other tests over a range of moderate to long-tailed symmetric distributions. The results also show that the test proposed by O'Gorman has greater power than the other tests for short-tailed distributions. For sample sizes greater than 50 and for small sample sizes the adaptive test proposed by O'Gorman has the highest power for most distributions.     

Exact tests for matched pairs:studies with covariates

In prospective or retrospective studies with matched pairs one often wishes to control for covariates other than those used in the matching process.Large sample procedures assuming a logistic model are available for this problem.The present paper presents some exact permutation tests which are uniformly most powerful unbiased within a large class of tests.     

A sequential approximation to a permutation test

A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated. Permutations are randomly generated from some set G, and a sequential probability ratio test (SPRT) is used to determine whether an observed test statistic falls sufficiently far in the tail of the permutation distribution to warrant rejecting some hypothesis. An estimate and bounds on the power function of the SPRT are used to find bounds on the effective significance level of the SAPT. Guidelines are developed for choosing parameters in order to obtain a desired significance level and minimize the number of permutations needed to reach a decision. A theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average number of permutations for various alternatives. The sequential approximation retains the generality of the permutation test,- while avoiding the computational complexities that arise in attempting to computer the full permutation distribution exactly     

A permutation test for randomness with power against smooth variation

A permutation test for the white noise hypothesis is described, offering power against a general class of smooth alternatives. Simulation results show that it performs well, as compared with similar tests available in the literature, in terms of power. An example demonstrates its use in a particular problem in which a test for randomness was sought without any specific alternative.     

Some exact tables for the squared ranks test

Since the squared ranks test was first proposed by Taha in 1964 it has been mentioned by several authors as a test that is easy to use, with good power in many situations. It is almost as easy to use as the Wilcoxon rank sum test, and has greater power when two populations differ in their scale parameters rather than in their location parameters. This paper discuss the versatility of the squared ranks test, introduces a test which uses squared ranks, and presents some exact tables     

A method for constructing exact tests from test statistics that have unknown null distributions

A randomized procedure is described for constructing an exact test from a test statistic F for which the null distribution is unknown. The procedure is restricted to cases where F is a function of a random element U that has a known distribution under the null hypothesis. The power of the exact randomized test is shown to be greater in some cases than the power of the exact nonrandomized test that could be constructed if the null distribution of Fwere known.     

Permuting incomplete paired data: a novel exact and asymptotic correct randomization test

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or homoscedasticity of the data. The aim of this paper is to develop a statistical test that is robust against deviations from such assumptions and also leads to valid inference in case of heteroscedasticity or skewed distributions. This is achieved by applying a clever randomization approach to handle missing data. The resulting test procedure is not only shown to be asymptotically correct but is also finitely exact if the distribution of the data is invariant with respect to the considered randomization group. Its small sample performance is further studied in an extensive simulation study and compared to existing methods. Finally, an illustrative data example is analysed.     

An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

A permutation test for the spread of three-dimensional rotation data

The permutation test is a nonparametric test that can be used to compare measures of spread for two data sets, but is yet to be explored in the context of three-dimensional rotation data. A permutation test for such data is developed and the statistical power of this test is considered under various conditions. The test is then used in a brief application comparing movement around the calcaneocuboid joint for a human, chimpanzee, and baboon.     

Multivariate multi-sample tests for location based on data depth

A notion of data depth is used to measure centrality or outlyingness of a data point in a given data cloud. In the context of data depth, the point (or points) having maximum depth is called as deepest point (or points). In the present work, we propose three multi-sample tests for testing equality of location parameters of multivariate populations by using the deepest point (or points). These tests can be considered as extensions of two-sample tests based on the deepest point (or points). The proposed tests are implemented through the idea of Fisher's permutation test. Performance of earlier tests is studied by simulation. Illustration with two real datasets is also provided.     

Multi-response permutation procedures for a priori classifications

An exact permutation test for analyzing and/or dredging multi-response data at the ordinal or higher levels is presented. The associated test statistic is based on the average distance (or any specified norm) between points within a priori disjoint subgroups of a finite population of points in an r-dimensional space (corresponding to r measured responses from each object in a finite population of objects). Alternative approximate tests based on the beta and normal distributions are provided. Two detailed examples utilizing actual social science data are considered, including comparisons of the approximate tests. An additional example describes the behavior of these tests under a variety of conditions, including extreme data configurations     

Rank invariant tests with left truncated and interval censored data

Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.     

Large sample results for permutation tests of association

This paper deals with the asymptotics of permutation tests based on a certain rather general class of measures of association for R by C contingency tables, given marginal totals. This class includes the classical chi-square test, the T _b and γ indices of Goodman and Kruskall (1954) and the popular Rand (1971) index. The asymptotic distribution of this class of permutation tests for association is a weighted sum of non-central (gen-erally speaking) chi-squares. The formulae for the asymptotic moments of such tests are also given. If non-centrality holds under the null hypothe-sis of independence, the distribution in question converges to the normal distribution. The efficacies for such measures of association are obtained. Several applications are analysed in detail, including the above mentioned indices. Approximations to the permutation distribution are also discussed.