Comparing distributions of time to onset of disease in animal tumorigenicity experiments

The cause-of-death test of Peto et al.(1980)pools information from a Hoel-Walburg test on incidental tumors with information from a logrank test on fatal tumors in order to compare the tumor rate of a group of rodents exposed to a carcinogen against the tumor rate of a group of unexposed animals. The cause-of-death test, which can arise as a partial likelihood score test from a model that assumes proportional odds for tumor prevalence and proportional hazards for tumor mortality, is not, in general, a direct test for equality of tumor onset distributions for occult tumors that are observed in both fatal and incidental contexts. This paper develops a direct cause-of-death test for comparing distributions of time to onset of occultumors. The test is derived as a partial likelihood score test under an assumed proportional hazards model for tumor onset distributions. The size and power of the proposed test are compared in a Monte Carlo simulation study to the size and power of competitive procedures, including procedures that do not require cause-of-death information.     

Tests for symmetry of two-piece normal distribution

In this paper, classical optimum tests for symmetry of two-piece normal distribution is derived. Uniformly most powerful one-sided test for the skewness parameter is obtained when the location and scale parameters are known and is compared with sequential probability ratio test. An ad-hoc test for symmetry and likelihood ratio test for symmetry for large samples, can be found in literature for this distribution. But in this paper, we derive exact likelihood ratio test for symmetry, when location parameter is known. The exact power of the test is evaluated for different sample sizes.     

Comparisons of various types of normality tests

Normality tests can be classified into tests based on chi-squared, moments, empirical distribution, spacings, regression and correlation and other special tests. This paper studies and compares the power of eight selected normality tests: the Shapiro–Wilk test, the Kolmogorov–Smirnov test, the Lilliefors test, the Cramer–von Mises test, the Anderson–Darling test, the D'Agostino–Pearson test, the Jarque–Bera test and chi-squared test. Power comparisons of these eight tests were obtained via the Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric short-tailed, symmetric long-tailed and asymmetric distributions. Our simulation results show that for symmetric short-tailed distributions, D'Agostino and Shapiro–Wilk tests have better power. For symmetric long-tailed distributions, the power of Jarque–Bera and D'Agostino tests is quite comparable with the Shapiro–Wilk test. As for asymmetric distributions, the Shapiro–Wilk test is the most powerful test followed by the Anderson–Darling test.     

Generalizations of Mathisen's median test for comparing several treatments with a control

A distribution-free test for comparing several treatments with a control is proposed for one-way classified data. It is advantageous to use the test in life-testing experiments where testing time is expensive. The proposed test has a shorter expected duration than a previously proposed test by Slivka(1970). The optimal allocation of the experimental units to the treatments for two situations are given. In a simulation study the power of the test is compared with the power of Slivka's test. An extension of the test for two-way classified data is given     

Power studies of tests for uniformity,II

Results from a power study of six statistics for testing that a sample is from a uniform distribution on the unit interval (0,1) are reported. The test statistics are all well-known and each of them was originally proposed because they should have high power against some alternative distributions. The tests considered are the Pearson probability product test, the Neyman smooth test, the Sukhatme test, the Durbin-Kolmogorov test, the Kuiper test, and the Sherman test. Results are given for each of these tests against each of four classes of alternatives. Also, the most powerful test against each member of the first three alternatives is obtained, and the powers of these tests are given for the same sample sizes as for the six general "omnibus" test statistics. These values constitute a "power envelope" against which all tests can be compared. The Neyman smooth tests with 2nd and 4th degree polynomials are found to have good power and are recommended as general tests for uniformity.     

An adaptive two-sample location-scale test of lepage type for symmetric distributions

For the two-sample location and scale problem we propose an adaptive test which is based on so called Lepage type tests. The well known test of Lepage (1971) is a combination of the Wilcoxon test for location alternatives and the Ansari-Bradley test for scale alternatives and it behaves well for symmetric and medium-tailed distributions. For the cae of short-, medium- and long-tailed distributions we replace the Wilcoxon test and the .Ansari-Bradley test by suitable other two-sample tests for location and scale, respectively, in oder to get higher power than the classical Lepage test for such distribotions. These tests here are called Lepage type tests. in practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes the the given data set inio consideration. The proposed adaptive test is based on the concept of Hogg (1974), i.e., first, to classify the unknown symmetric distribution function with respect to a measure for tailweight and second, to apply an appropriate Lepage type test for this classified type of distribution. We compare the adaptive test with the three Lepage type tests in the adaptive scheme and with the classical Lepage test as well as with other parametric and nonparametric tests. The power comparison is carried out via Monte Carlo simulation. It is shown that the adaptive test is the best one for the broad class of distributions considered.     

Testing for superadditivity of the mean value function of a non-homogeneous poisson process

Consider a non-homogeneous Poisson process, N(t), with mean value function Λ(t) and intensity function λ(t). A conditional test of the hypothesis that the process is homogeneous, versus alternatives for which Λ(t) is superadditive, was proposed by Hollander and Proschan (1974). A new test for superadditivity of Λ(t), which is based on a linear combination of the occurrence times of the process N{t) is suggested in this paper. Though this test has the same Pitman efficiency as the Hollander-Proschan test, it is shown by Monte-Carlo simulation that our test has more power for many important alternatives. Tables for the exact null distribution of the test statistic have been given.     

The limit test statistic distribution of the maximum value test for right-censored data

ABSTRACT

In this paper, the maximum value test is proposed and considered for two-sample problem solving with lifetime data. This test is a distribution-free test under non-censoring and is a not distribution-free test under censoring. The formula of the limit distribution of the proposed maximal value test is represented in the general case. The distribution of the test statistic has been studied experimentally. Also, we propose the estimate of a p-value calculation of the maximum value test instead of the Monte-Carlo simulation. This test is useful and applicable in case of choosing among the logrank test, the Cox–Mantel test, the Q test and Generalized Wilcoxon tests, for instance, the Gehan's Generalized Wilcoxon test and the Peto and Peto's Generalized Wilcoxon test.     

Testing the Equality of Two Exponential Distributions

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzman's overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.     

A modified chi-square test of independence against a class of ordered alternatives in an r x c contingency table

A modified chi-square test statistic is constructed for testing the hypothesis of independence in a two-way contingency table against a class of ordered alternatives defined in terms of pooled cross-product ratios. The test procedure can also be used to test for positive quadrant dependence in a two-way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.     

One sample tests of location for nonnormal symmetric data

A score test of location is derived for data from a distorted normal distribution. A simulation study compares the performance of this test to the t-test and Wilcoxon test for symmetric data from such a distribution. For this type of data the score test can be considerably more powerful than both the t-test and Wilcoxon test. This suggests that such a score test may be useful in practice when variations from normality can be modeled by such a family of distributions.     

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.     

Empirical phi-divergence test statistics for the difference of means of two populations

Empirical phi-divergence test statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behavior of the classical likelihood ratio test statistic, as well as for model misspecification problems, in both cases for the one population problem. This paper introduces this methodology for two-sample problems. A simulation study illustrates situations in which the new test statistics become a competitive tool with respect to the classical z test and the likelihood ratio test statistic.     

ADF模式中漂移项和趋势项检验量分布与Bootstrap检验研究

在推导ADF检验模式下趋势项和漂移项伪t检验量极限分布基础上,提出修正的系数检验量。研究表明,它们与DF检验模式下检验量具有相同的极限分布;构造漂移项和趋势项检验的Bootstrap实现方法并证明了有效性。将蒙特卡洛模拟技术与临界值检验方法进行对比,结果表明Bootstrap方法能够明显降低检验的水平扭曲,在检验功效方面也有一定优势。模拟也显示临界值检验的局限性和Bootstrap方法的稳健性。     

Reweighted Smooth Tests of Goodness of Fit

Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the different directions in the space of alternatives, the reweighted smooth test makes a distinction in importance of the directions. The advantage of this test, as opposed to directional tests, is that the smooth character is largely maintained. We discuss both nested and non nested directional alternatives.     

Power and robustness of sib-pair linkage tests and extension to larger sibships

We investigate the power and robustness of Haseman and Elstonfs sib-pair test for genetic linkage between a marker locus and a locus affecting a quantitative trait, and compare the test to that of Penrose. The Haseman-Elston test is more powerful than Penrrose's test; its power is acceptable for cases of tight linkage and high heritability due to the hypothesized quantitative trait locus, but is quite low in other situations. Computer simulations indicate that both tests are valid for normally distributed trait values, and that the Haseman-Elston test is robust for a variety of continuous distributions of the trait values. Several linkage tests are developed for sib trios that are much more powerful , for the same total number of sibs, than the test on independent sib pairs. The Haseman-Elston test on all possible sib pairs is suggested for sibships of size larger than three and for samples including sibships of various sizes.     

Locally optimal test of normality against skew-normality

Efficient Score testing procedures for testing for the skewness parameter of the one-parameter and three-parameter skew-normal distributions are investigated. Approximate percentage points for the test statistics are obtained via the Monte Carlo method. Salvan's locally optimal test is extended and simulation is used to show that the power of the extended test is higher than that of the skewness test.     

Evaluating the power of Minitab's data subsetting lack of fit test in multiple linear regression

Minitab's data subsetting lack of fit test (denoted XLOF) is a combination of Burn and Ryan's test and Utts' test for testing lack of fit in linear regression models. As an alternative to the classical or pure error lack of fit test, it does not require replicates of predictor variables. However, due to the uncertainty about its performance, XLOF still remains unfamiliar to regression users while the well-known classical lack of fit test is not applicable to regression data without replicates. So far this procedure has not been mentioned in any textbooks and has not been included in any other software packages. This study assesses the performance of XLOF in detecting lack of fit in linear regressions without replicates by comparing the power with the classic test. The power of XLOF is simulated using Minitab macros for variables with several forms of curvature. These comparisons lead to pragmatic suggestions on the use of XLOF. The performance of XLOF was shown to be superior to the classical test based on the results. It should be noted that the replicates required for the classical test made itself unavailable for most of the regression data while XLOF can still be as powerful as the classic test even without replicates.     

Tests of Symmetry in Three-dimensional Contingency Tables Based on Phi-divergence Statistics

In this paper we introduce a family of test statistics for testing complete symmetry in three-dimensional contingency tables based on phi- divergence families. These test statistics yield the likelihood ratio test and the Pearson test statistics as special cases. Asymptotic distribution for the new test statistics are derived under both the null and the alternative hypotheses. A simulation study is presented to show that some new statistics offer an attractive alternative to the classical Pearson and likelihood ratio test statistics for this problem of complete symmetry.     

Tables of critical values of the normal probability paper test

The present paper relates to Holm's normal probability paper test for simple hypotheses. It is shown how to obtain the statistics for the one-sided and two-sided tests using normal probability paper. Tables of critical values of these test statistics are given for practical use of the test; the equations for calculating the distribution functions of the test statistics are listed. Two different methods lead to these equations; but details are beyond the scope of the present paper and the interested reader is referred to another paper.