• Communications for Statistical Applications and Methods
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• 제5권1호
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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 the Korean Data and Information Science Society
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• 제15권1호
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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 Statistical Society
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• 제27권2호
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• pp.197-203
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• 1998

To test the hypothesis of complete or total independence for a multi-way contingency table, the Pearson chi-squared test statistic is usually employed under Poisson or multinomial models. It is well known that, under the hypothesis, this statistic follows an asymptotic chi-squared distribution. We consider the case where all marginal sums of the contingency table are fixed. Using conditional limit theorems, we show that the chi-squared test statistic has the same limiting distribution for this case.

• Communications for Statistical Applications and Methods
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• 제10권1호
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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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• 제3권2호
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• pp.69-76
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• 1996

In a two-way contingency table, the analyst is most interested in the hypotheses of either homogeneity or independence. For testing this as a null hypothesis, Pearson's ${\chi}^2$ statistic is most commonly used in practice. Once the null Hypothesis is rejected, he will further search forcells which caused the rejection of the null hypothesis. For this purpose, so called cell${\chi}^2$ components are used. In this paper, we derive the influence function of an obsevation to the ${\chi}^2$ statistic, with which cells with high influence can be identified.

• Journal of the Korean Data and Information Science Society
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• 제17권2호
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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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• 제7권2호
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• pp.403-414
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• 2000

A diagnostic tool for testing homogeneity for random effects is proposed in unbalanced linear mixed model based on score statistic. The finite sample behavior of the test statistic is examined using Monte Carlo experiments examine the chi-square approximation of the test statistic under the null hypothesis.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.51-63
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• 2001

We are interested in the conditional independence in sparse $2\tims2\tims$K tables with very rare cell counts. The most popular test is Cochran-Mantel-Haenszel statistic when sample sizes are moderately large enough to guarantee the chi-square approximation. We will consider jackknifing the CMH test and also suggest an approximate normal distribution for the standardized jackknifed CMH statistic. The main focus of this paper is to improve the chi-squared approximation to the CMH test by using the asymptotic normality of the jackknifed CMH test when sample sizes are very sparse but K and N$\infty$. The performance of the proposed jackknifed test, in the sense of significance level control and power, will be compared with that of the CMH test through a Monte Carlo study.

• Communications for Statistical Applications and Methods
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• 제7권2호
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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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• 제5권2호
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• pp.411-416
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• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.