Marking scheme for the test for logical order in English language testing:is it fair?

This note discusses a marking scheme for resting a student's ability to order English language sentences in a logical manner. It is shown that, in some circumstances, a student of intermediate ability may have a lower probability of obtaining a pass score than would a student of poor ability who guesses the order of all the sentences.     

A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

Likelihood ratio test for testing order of continuous time finite markov chains

Anderson and Goodman ( 1957) have obtained the likelihood ratio tests and chi-square tests for testing the hypothesis about the order of discrete time finite Markov chains, On the similar lines we have obtained likeli¬hood ratio tests and chi-square tests (asymptotic) for testing hypotheses about the order of continuous time Markov chains (MC) with finite state space.     

A modified chi-square test for testing equality of two multinomial populations against an order restricted alternative

A modified chi-square test for testing the equality of two multinomial populations against an order restricted alternative in one sample and two sample cases is constructed. The relation between the concepts of dependence by cM-square and stochastic ordering is established, The asymptotic distribution of the test statistic is the chi-bar-square type discussed by Robertson, Wright and Dykstra (1988). Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations.     

A test for second order stochastic dominance

In this paper we propose a test for second order stochastic dominance (SSD), for the case where both distribution functions are unknown. This is a generalization of a test proposed by Deshpande and Singh (1985), who compare a new random prospect with a known distribution function. We then show that our test is based on comparing the mean minus one half of Gini's mean difference of the distributions, which is known to be a necessary condition for SSD, as developed in the economics literature (Yitzhaki, 1982).     

The twelfth order analogue of the durbin-watson test

This paper provides five percent significance bounds on critical values of the twelfth or-der analogue of the Durbin-Watsontest. These tables are useful for testing for twelfth order autocorrelation in regression models with monthly data which include either an intercept or a full set of monthly seasonal dummies.     

Preliminary test estimation for the second order autoregression

Consequences of preliminary test model identification procedures in time series analysis are examined in the context of a squared error risk function. Asymptotic risk comparisons and Monte Carlo studies are used in comparing these procedures.     

On nonparametric test for the residual probability order

Residual probability order is a partial ordering analog of the total order stochastic precedence which can be fruitfully applied in many reliability problems. We introduce a U-statistic test for the null hypothesis that two random variables are equally distributed versus the alternative that one strictly dominates the other in residual probability order. The critical value is obtained by normal approximation and bootstrap procedures. The performance of the test statistic is evaluated using a simulation study. Finally, a numerical example illustrating the theory is also given.     

On gart's test for interaction of second order

Gart (1972) ottered a Statistic on testing the hypothesis of no second-order interaction in a 2×s×t contingency table. The statistic was tn be used as an asymptotic chi-square with (s-1) (t-1) degrees of freedom. We show that this statistic suiters from the drawback that unless certain side conditions hold, the statistic would reject the null hypothesis with probability approaching one asymptotically even in the null case. Hence the statistic is not strictly valid for the hypothesis for which it was intended.     

The likelihood ratio test for simple tree order: A useful asymptotic expansion

We derive new approximations for the likelihood ratio statistics that are used in testing hypotheses involving simple tree order. They are based on asymptotics when the number of populations tends to infinity and variances are equal.As an application quantiles are obtained that are much easier to calculate than exact critical values or the gamma-approximation usually proposed in literature. Our quantitles also provide often better approximations than those known in literature.     

Multivariate testing and model-checking for generalized order statistics with applications

The exponential family structure of the joint distribution of generalized order statistics is utilized to establish multivariate tests on the model parameters. For simple and composite null hypotheses, the likelihood ratio test (LR test), Wald's test, and Rao's score test are derived and turn out to have simple representations. The asymptotic distribution of the corresponding test statistics under the null hypothesis is stated, and, in case of a simple null hypothesis, asymptotic optimality of the LR test is addressed. Applications of the tests are presented; in particular, we discuss their use in reliability, and to decide whether a Poisson process is homogeneous. Finally, a power study is performed to measure and compare the quality of the tests for both, simple and composite null hypotheses.     

Tests for the total time on test transform order

In this paper we consider two test statistics for testing the strict TTT transform order between two life distributions of interest. We give their asymptotic distributions and compare our tests with some other related tests in terms of Pitman's asymptotic efficiency. Also we present some results to show the performance and the asymptotic normality of our tests.     

On a test for exponentiality against Laplace order dominance

Surles and Padgett recently introduced two-parameter Burr Type X distribution, which can also be described as the generalized Rayleigh distribution. It is observed that the generalized Rayleigh and log-normal distributions have many common properties and both the distributions can be used quite effectively to analyze skewed data set. For a given data set the problem of selecting either generalized Rayleigh or log-normal distribution is discussed in this paper. The ratio of maximized likelihood (RML) is used in discriminating between the two distributing functions. Asymptotic distributions of the RML under null hypotheses are obtained and they are used to determine the minimum sample size required in discriminating between these two families of distributions for a used specified probability of correct selection and the tolerance limit.     

A robust test for testing the correlation coefficient

A test based on Tiku's MML (modified maximum likelihood) estimators is developed for testing that the population correlation coefficient is zero. The test is compared with various other tests and shown to have good Type I error robustness and power for numerous symmetric and skew bivariate populations.     

Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative

In applications of generalized order statistics as, for instance, reliability analysis of engineering systems, prior knowledge about the order of the underlying model parameters is often available and may therefore be incorporated in inferential procedures. Taking this information into account, we establish the likelihood ratio test, Rao's score test, and Wald's test for test problems arising from the question of appropriate model selection for ordered data, where simple order restrictions are put on the parameters under the alternative hypothesis. For simple and composite null hypothesis, explicit representations of the corresponding test statistics are obtained along with some properties and their asymptotic distributions. A simulation study is carried out to compare the order restricted tests in terms of their power. In the set-up considered, the adapted tests significantly improve the power of the associated omnibus versions for small sample sizes, especially when testing a composite null hypothesis.     

A modified test for testing exponentiality using transformed data

In this article, we present a test for testing uniformity. Based on the test, we provide a test for testing exponentiality. Empirical critical values for both the tests are computed. Both the tests are compared with the tests proposed by Noughabi and Arghami [H. Alizadeh Noughabi, and N.R. Arghami, Testing exponentiality using transformed data, J. Statist. Comput. Simul. 81 (4) (2011), pp. 511–516] using simulation experiments for a wide class of alternatives. The tests possess attractive power properties.     

On an ad hoc test for order restricted multivariate normal means

Abstract

For several normal mean vectors restricted by a simple ordering with respect to a multivariate order, this article derives sufficient and necessary conditions for the restricted MLEs for both mean vectors and covariance matrix, and develops an ad hoc test. It establishes conditions for the bounds of the p-values. One example of such bound is given with some comments.     

A combined p-value test for multiple hypothesis testing

Tests that combine p-values, such as Fisher's product test, are popular to test the global null hypothesis H₀ that each of n component null hypotheses, H₁,…,H_n, is true versus the alternative that at least one of H₁,…,H_n is false, since they are more powerful than classical multiple tests such as the Bonferroni test and the Simes tests. Recent modifications of Fisher's product test, popular in the analysis of large scale genetic studies include the truncated product method (TPM) of Zaykin et al. (2002), the rank truncated product (RTP) test of Dudbridge and Koeleman (2003) and more recently, a permutation based test—the adaptive rank truncated product (ARTP) method of Yu et al. (2009). The TPM and RTP methods require users' specification of a truncation point. The ARTP method improves the performance of the RTP method by optimizing selection of the truncation point over a set of pre-specified candidate points. In this paper we extend the ARTP by proposing to use all the possible truncation points {1,…,n} as the candidate truncation points. Furthermore, we derive the theoretical probability distribution of the test statistic under the global null hypothesis H₀. Simulations are conducted to compare the performance of the proposed test with the Bonferroni test, the Simes test, the RTP test, and Fisher's product test. The simulation results show that the proposed test has higher power than the Bonferroni test and the Simes test, as well as the RTP method. It is also significantly more powerful than Fisher's product test when the number of truly false hypotheses is small relative to the total number of hypotheses, and has comparable power to Fisher's product test otherwise.     

Most mean powerful invariant test for testing two-dimensional parameter spaces

This paper investigates the application of the most mean powerful invariant test to the problem of testing for joint MA(1)–MA(4) disturbances against joint AR(1)–AR(4) disturbances in the linear regression model. The most mean powerful invariant test was introduced by Begum and King (Most mean powerful invariant test of a composite null against a composite alternative. Comp. Statist. Data Analysis, 2004, forthcoming) and is based on the generalized Neyman–Pearson lemma which provides an optimal test of certain composite hypotheses. The most mean powerful invariant test can be computationally intensive. Previous applications have only involved testing problems whose null hypotheses, after reduction through invariance arguments, are one dimensional. This is the first application involving null and alternative hypotheses which are two dimensional. A Monte Carlo experiment was conducted to assess the small sample performance of the test with encouraging results. The increase in dimension does increase significantly the computational effort required to apply the test.     

Bain: a program for Bayesian testing of order constrained hypotheses in structural equation models

This paper presents a new statistical method and accompanying software for the evaluation of order constrained hypotheses in structural equation models (SEM). The method is based on a large sample approximation of the Bayes factor using a prior with a data-based correlational structure. An efficient algorithm is written into an R package to ensure fast computation. The package, referred to as Bain, is easy to use for applied researchers. Two classical examples from the SEM literature are used to illustrate the methodology and software.