Nonparametric tests for multivariate multi-sample locations based on data depth

Several nonparametric tests for multivariate multi-sample location problem are proposed in this paper. These tests are based on the notion of data depth, which is used to measure the centrality/outlyingness of a given point with respect to a given distribution or a data cloud. Proposed tests are completely nonparametric and implemented through the idea of permutation tests. Performance of the proposed tests is compared with existing parametric test and nonparametric test based on data depth. An extensive simulation study reveals that proposed tests are superior to the existing tests based on data depth with regard to power. Illustrations with real data are provided.     

Unconditional analogues of Cochran–Mantel–Haenszel tests

The Cochran–Mantel–Haenszel tests are a suite of tests that are usually defined as conditional tests, tests that assume all marginal totals are known before sighting the data. Here unconditional analogues of these tests are defined for the more usual situation when the marginal totals are not known before sighting the data.     

Permutational tests for correlation matrices

Permutational tests are proposed for the hypotheses that two population correlation matrices have common eigenvectors, and that two population correlation matrices are equal. The only assumption made in these tests is that the distributional form is the same in the two populations; they should be useful as a prelude either to tests of mean differences in grouped standardised data or to principal component investigation of such data.The performance of the permutational tests is subjected to Monte Carlo investigation, and a comparison is made with the performance of the likelihood-ratio test for equality of covariance matrices applied to standardised data. Bootstrapping is considered as an alternative to permutation, but no particular advantages are found for it. The various tests are applied to several data sets.     

Monte carlo results for conditional survival tests under randomly censored data

Within a Monte Carlo study finite sample results are obtained for different generalized rank tests based on randomly censored life time data. It is pointed out that conditional tests should be applied in practice whenever drastic differences between the censoring distributions for the underlying groups do not appear. The tests are slight modifications of known permutation tests for censored data.     

Multivariate two‐sample permutation tests for trials with multiple time‐to‐event outcomes

Clinical trials involving multiple time‐to‐event outcomes are increasingly common. In this paper, permutation tests for testing for group differences in multivariate time‐to‐event data are proposed. Unlike other two‐sample tests for multivariate survival data, the proposed tests attain the nominal type I error rate. A simulation study shows that the proposed tests outperform their competitors when the degree of censored observations is sufficiently high. When the degree of censoring is low, it is seen that naive tests such as Hotelling's T² outperform tests tailored to survival data. Computational and practical aspects of the proposed tests are discussed, and their use is illustrated by analyses of three publicly available datasets. Implementations of the proposed tests are available in an accompanying R package.     

Power comparison of data depth-based nonparametric tests for testing equality of locations

In the recent years, the notion of data depth has been used in nonparametric multivariate data analysis since it gives natural ‘centre-outward’ ordering of multivariate data points with respect to the given data cloud. In the literature, various nonparametric tests are developed for testing equality of location of two multivariate distributions based on data depth. Here, we define two nonparametric tests based on two different test statistic for testing equality of locations of two multivariate distributions. In the present work, we compare the performance of these tests with the tests developed by Li and Liu [New nonparametric tests of multivariate locations and scales using data depth. Statist Sci. 2004;(1):686–696] for testing equality of locations of two multivariate distributions. Comparison in terms of power is done for multivariate symmetric and skewed distributions using simulation for three popular depth functions. Application of tests to real life data is provided. Conclusion and recommendations are also provided.     

Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model data and then it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the IG goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. These tests are consistent against all alternatives. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by real data examples.     

Goodness-of-fit tests for progressively Type-II censored data from location–scale distributions

In this article, we propose several goodness-of-fit methods for location–scale families of distributions under progressively Type-II censored data. The new tests are based on order statistics and sample spacings. We assess the performance of the proposed tests for the normal and Gumbel models against several alternatives by means of Monte Carlo simulations. It has been observed that the proposed tests are quite powerful in comparison with an existing goodness-of-fit test proposed for progressively Type-II censored data by Balakrishnan et al. [Goodness-of-fit tests based on spacings for progressively Type-II censored data from a general location–scale distribution, IEEE Trans. Reliab. 53 (2004), pp. 349–356]. Finally, we illustrate the proposed goodness-of-fit tests using two real data from reliability literature.     

Tests for outliers in the inverse Gaussian distribution,with application to first hitting time models

The inverse Gaussian (IG) distribution is often applied in statistical modelling, especially with lifetime data. We present tests for outlying values of the parameters (μ, λ) of this distribution when data are available from a sample of independent units and possibly with more than one event per unit. Outlier tests are constructed from likelihood ratio tests for equality of parameters. The test for an outlying value of λ is based on an F-distributed statistic that is transformed to an approximate normal statistic when there are unequal numbers of events per unit. Simulation studies are used to confirm that Bonferroni tests have accurate size and to examine the powers of the tests. The application to first hitting time models, where the IG distribution is derived from an underlying Wiener process, is described. The tests are illustrated on data concerning the strength of different lots of insulating material.     

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.     

A Comparative Study of Model-based Tests of Independence for Ordinal Data Using the Bootstrap

When analyzing categorical data using loglinear models in sparse contingency tables, asymptotic results may fail. In this paper the empirical properties of three commonly used asymptotic tests of independence, based on the uniform association model for ordinal data, are investigated by means of Monte Carlo simulation. Five different bootstrapped tests of independence are presented and compared to the asymptotic tests. The comparisons are made with respect to both size and power properties of the tests. Results indicate that the asymptotic tests have poor size control. The test based on the estimated association parameter is severely conservative and the two chi-squared tests (Pearson, likelihood-ratio) are both liberal. The bootstrap tests that either use a parametric assumption or are based on non-pivotal test statistics do not perform better than the asymptotic tests in all situations. The bootstrap tests that are based on approximately pivotal statistics provide both adjustment of size and enhancement of power. These tests are therefore recommended for use in situations similar to those included in the simulation study.     

The Perils of Balance Testing in Experimental Design: Messy Analyses of Clean Data

Widespread concern over the credibility of published results has led to scrutiny of statistical practices. We address one aspect of this problem that stems from the use of balance tests in conjunction with experimental data. When random assignment is botched, due either to mistakes in implementation or differential attrition, balance tests can be an important tool in determining whether to treat the data as observational versus experimental. Unfortunately, the use of balance tests has become commonplace in analyses of “clean” data, that is, data for which random assignment can be stipulated. Here, we show that balance tests can destroy the basis on which scientific conclusions are formed, and can lead to erroneous and even fraudulent conclusions. We conclude by advocating that scientists and journal editors resist the use of balance tests in all analyses of clean data. Supplementary materials for this article are available online     

Nonparametric tests for multivariate locations based on data depth

The present paper deals with the problem of testing equality of locations of two multivariate distributions using a notion of data depth. A notion of data depth has been used to measure centrality/outlyingness of a given point in a given data cloud. The paper proposes two nonparametric tests for testing equality of locations of two multivariate populations which are developed by observing the behavior of the depth versus depth plot. Simulation study reveals that the proposed tests are superior to the existing tests based on the data depth with regard to power. Illustrations with real data are provided.     

Detecting Randomness: A Review of Existing Tests with New Comparisons

In this article we review and compare a number of existing tests for detecting randomness in time series data, with emphasis on stock market index data. By comparing variance ratio tests with traditional statistical tests, we have the most extensive simulation comparison of such procedures. The investigated tests are compared over a diverse group of distributions, models, and stock market applications. In our stock market data analysis, the choice of data transformation can have a noticeable effect on test results. This study provides the reader with a guide as to which test and transformation is most appropriate for their use.     

Adjusted homogeneity tests of odds ratios when data are clustered

Three modified tests for homogeneity of the odds ratio for a series of 2 × 2 tables are studied when the data are clustered. In the case of clustered data, the standard tests for homogeneity of odds ratios ignore the variance inflation caused by positive correlation among responses of subjects within the same cluster, and therefore have inflated Type I error. The modified tests adjust for the variance inflation in the three existing standard tests: Breslow–Day, Tarone and the conditional score test. The degree of clustering effect is measured by the intracluster correlation coefficient, ρ. A variance correction factor derived from ρ is then applied to the variance estimator in the standard tests of homogeneity of the odds ratio. The proposed tests are an application of the variance adjustment method commonly used in correlated data analysis and are shown to maintain the nominal significance level in a simulation study. Copyright © 2004 John Wiley & Sons, Ltd.     

Correlation-adjusted estimation of sensitivity and specificity of two diagnostic tests

Summary. Models for multiple-test screening data generally require the assumption that the tests are independent conditional on disease state. This assumption may be unreasonable, especially when the biological basis of the tests is the same. We propose a model that allows for correlation between two diagnostic test results. Since models that incorporate test correlation involve more parameters than can be estimated with the available data, posterior inferences will depend more heavily on prior distributions, even with large sample sizes. If we have reasonably accurate information about one of the two screening tests (perhaps the standard currently used test) or the prevalences of the populations tested, accurate inferences about all the parameters, including the test correlation, are possible. We present a model for evaluating dependent diagnostic tests and analyse real and simulated data sets. Our analysis shows that, when the tests are correlated, a model that assumes conditional independence can perform very poorly. We recommend that, if the tests are only moderately accurate and measure the same biological responses, researchers use the dependence model for their analyses.     

A multivariate zero-inflated binomial model for the analysis of correlated proportional data

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.     

Multivariate analysis of variance for functional data

Functional data are being observed frequently in many scientific fields, and therefore most of the standard statistical methods are being adapted for functional data. The multivariate analysis of variance problem for functional data is considered. It seems to be of practical interest similarly as the one-way analysis of variance for such data. For the MANOVA problem for multivariate functional data, we propose permutation tests based on a basis function representation and tests based on random projections. Their performance is examined in comprehensive simulation studies, which provide an idea of the size control and power of the tests and identify differences between them. The simulation experiments are based on artificial data and real labeled multivariate time series data found in the literature. The results suggest that the studied testing procedures can detect small differences between vectors of curves even with small sample sizes. Illustrative real data examples of the use of the proposed testing procedures in practice are also presented.     

Exact Tests in Panel Data Using Generalized p-Values

In this article, we consider exact tests in panel data regression model with one-way and two-way error component for which no exact tests are available. Exact inferences using generalized p-values are obtained. When there are several groups of panel data, test for equal coefficients under one-way and two-way error component are derived.     

Measurement Errors and Tests for Rationality

The traditional tests for rationality, the regression and volatility tests, have often rejected the hypothesis of rationality for survey data on expectations. It has been argued that these tests are not valid in the presence of unit roots and hence cointegration tests should be applied. The cointegration tests have often failed to reject the hypothesis of rationality. The present article argues that errors in variables affect tests of rationality. We use multiple sources of expectations to correct for the errors-in-variables bias but find that the hypothesis of rationality is rejected even after this correction. The article uses survey data on interest rates, stock prices, and exchange rates.