• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.381-391
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• 1996

In the analysis of contingency table with ordered categories, the relationship between odds for adjacent categories has received con-siderable interest. We consider likelihood ratio tests of independence against an order restriction on odds in 2 $\times$ k contingency tables.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.305-317
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• 2003

We suggest methods to measure the changes in $x^2$ statistic when a row is deleted from a two-way contingency table. The influence function is extended and the deletion method is applied. Two examples are presented and we compare the results obtained from the influence function method and the deletion method.

• Journal of the Korean Statistical Society
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• v.13 no.1
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• pp.1-19
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• 1984

A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.129-147
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• 2004

For square contingency tables with nominal categories, this paper proposes a measure to represent the degree of departure from the quasi-symmetry (QS) model and the Bradley-Terry (BT) model. The measure proposed is expressed by using the Cressie and Read (1984)'s power-divergence or Patil and Taillie (1982)'s diversity index. The measure lies between 0 and 1, and it is useful for comparing the degree of departure from QS or BT in several tables.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.289-303
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• 1998

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.495-500
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• 2012

We consider a Bayesian test of independence in a two-way contingency table that has some zero cells. To do this, we take a three-stage hierarchical Bayesian model under each hypothesis. For prior, we use Dirichlet density to model the marginal cell and each cell probabilities. Our method does not require complicated computation such as a Metropolis-Hastings algorithm to draw samples from each posterior density of parameters. We draw samples using a Gibbs sampler with a grid method. For complicated posterior formulas, we apply the Monte-Carlo integration and the sampling important resampling algorithm. We compare the values of the Bayes factor with the results of a chi-square test and the likelihood ratio test.

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.339-352
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• 1997

Chi-square test based on large sample theory is inappropriate for testing the row homogeneity in two-way contingency table with several sparse cells. For that case, exact testing methods has been developed in the literature and implemented in StatXact(1991). However, considerable computing time is inevitable for moderate size tables. So, Monte Carlo approximation is recommended frequently. In this study, we propose a simple algorithm for generating two-way random tables with fixed row and column margins for small sample chi-square test. Also, we develop “Turkey-type” method for multiple between-row comparisons.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.337-346
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• 2004

The Pearson chi-square goodness-of-fit test and the likelihood ratio tests are usually used for testing independence in two-way contingency tables under random sampling. But both of these tests may provide false results for the contingency table with clustered observations. In this case we consider the generalized linear mixed model which includes random effects of clustering in addition to the fixed effects of covariates. Both the heterogeneity between clusters and the dependency within a cluster can be explained via generalized linear mixed model. In this paper we introduce several types of generalized linear mixed model for testing independence in contingency tables with clustered observations. We also discuss the fitting of these models through a real dataset.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.89-103
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• 2004

If the given information is exact, though it is the little, we had better use it than not use in analysis. In this article, the problem of independence test in a contingency table is considered when two marginal distributions of a population are given exactly. For that case, a likelihood-ratio chi-squared test statistic and its Pearsonian type chi-squared test statistic are derived. By Monte Carlo Simulations the traditional chi-square tests and the derived tests are compared. And the related some testing problems are synthetically explained on a geometrical viewpoint.

• 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.