• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.211-218
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• 2004

The subject of assessing whether a data set is from a specific distribution has received a good deal of attention. This topic is critically important for uniform distributions. Several parametric tests are compared. These tests also can be used in testing randomness of a sample. Anderson-Darling $A^2$ statistic is found to be most powerful.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.135-144
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• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.35-42
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• 1998

Once a contingency table is constructed, the first interest will be the hypotheses of either homogeneity or independence depending on the sampling scheme. The most widely used test statistic in practice is the classical Pearson's $\chi^2$ statistic. When the null hypothesis is rejected, another natural interest becomes which cell contributed to the rejection of the null hypothesis more than others. For this purpose, so called cell $\chi^2$ components are investigated. In this paper, the influence function of a cell to the $\chi^2$ statistic is derived, which can be used for the same purpose. This function measures the effect of each cell to the $\chi$$^2$ statistic. A numerical example is given to demonstrate the role of the new function.

• Journal of Integrative Natural Science
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• v.7 no.3
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• pp.208-213
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• 2014

National-wide and/or large scale sample surveys generally use complex sample design. Traditional Pearson chi-square test is not appropriate for the categorical complex sample data. Rao-Scott suggested an adjustment method for Pearson chi-square test, which uses the average of eigenvalues of design matrix of cell probabilities. This study is to compare the efficiency of Rao-Scott first order adjusted test to Wald test for homogeneity between two populations using 2009 Gyeongnam regional education offices's customer satisfaction survey (2009 GREOCSS) data. The 2009 GREOCSS data were collected based on stratified three-stage cluster sampling with probability proportional to size. The empirical results show that the Rao-Scott adjusted test statistic using only the variances of cell probabilities is very close to the Wald test statistic, which uses the covariance matrix of cell probabilities, under the 2009 GREOCSS data based. However it is necessary to be cautious to use the Rao-Scott first order adjusted test statistic in the place of Wald test because its efficiency is decreasing as the relative variance of eigenvalues of the design matrix of cell probabilities is increasing, specially more when the number of degrees of freedom is small.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.455-467
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• 2003

There has been a long debate on the applicability of the chi-square approximation to statistics based on small sample size. Extending comparison results among Pearson chi-square Χ$^2$, generalized likelihood .ratio G$^2$, and the power divergence Ι(2/3) statistics suggested by Rudas(1986), recently developed disparity statistics (BWHD(1/9), BWCS(1/3), NED(4/3)) we compared and analyzed in this paper. By Monte Carlo studies about the independence model of two dimension contingency tables, the conditional model and one variable independence model of three dimensional tables, simulated 90 and 95 percentage points and approximate 95% confidence intervals for the true percentage points are obtained. It is found that the Χ$^2$, Ι(2/3), BWHD(1/9) test statistics have very similar behavior and there seem to be applcable for small sample sizes than others.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1057-1065
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• 2010

In this paper we discuss some cautionary notes in using the Pearson chi-squared test statistic for the goodness-of-fit of the ordinal response model. If a model includes continuous type explanatory variables, the resulting table from the t of a model is not a regular one in the sense that the cell boundaries are not fixed but randomly determined by some other criteria. The chi-squared statistic from this kind of table does not have a limiting chi-square distribution in general and we need to be very cautious of the use of a chi-squared type goodness-of-t test. We also study the limiting distribution of the chi-squared type statistic for testing the goodness-of-t of cumulative logit models with ordinal responses. The regularity conditions necessary to the limiting distribution will be reformulated in the framework of the cumulative logit model by modifying those of Moore and Spruill (1975). Due to the complex limiting distribution, a parametric bootstrap testing procedure is a good alternative and we explained the suggested method through a practical example of an ordinal response dataset.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.609-620
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• 2005

In the secondary data analysis for categorical data, situations often arise in which the estimated cell variances are available, but not the full matrix of variances. In this case researchers are often inclined to use Pearson-type test statistics for homogeneity. However, for a complex sample observed cell proportions are not distributed as multinomial and Pearson-type test statistic generally is not distributed asymptotically as chi-square distribution. This paper evaluates powers for Wald test and Pearson-type test and the first order corrected test of Pearson-type test for homogeneity. The resulting power curves indicate that as the misspecification effect increases, the amount of inflation of significance level and the loss of power Pearson-type test are getting more severe.