• Journal of Korean Society for Quality Management
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• v.12 no.2
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• pp.11-14
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• 1984

Some statistics are presented for construction of confidence intervals of variance components for the unbalanced twofold nested classification model and they are shown to be approximated by chi-square distributions.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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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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• v.8 no.3
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• pp.603-613
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• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• 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.

• 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.29 no.1
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• pp.1-25
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• 2022

A modified Bagdonavičius-Nikulin chi-square goodness-of-fit is defined and studied. The lymphoma data is analyzed using the modified goodness-of-fit test statistic. Different non-Bayesian estimation methods under complete samples schemes are considered, discussed and compared such as the maximum likelihood least square estimation method, the Cramer-von Mises estimation method, the weighted least square estimation method, the left tail-Anderson Darling estimation method and the right tail Anderson Darling estimation method. Numerical simulation studies are performed for comparing these estimation methods. The potentiality of the new model is illustrated using three real data sets and compared with many other well-known generalizations.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• The Journal of Korean Academy of Prosthodontics
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• v.30 no.2
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• pp.273-285
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• 1992

The purpose of this study was to evaluate facial form, arch form and tooth form in young adults to determine if a correlation exists. 115 subjects who had healthy natural maxillary incisors and good occlusion consisted of 71 males and 44 females ranging from 20-30 years of age. Facial photographs and, intraoral photographs of upper anterior teeth and dental casts of upper jaws were taken to demonstrate facial form, dental arch form and tooth form. Form analysis is determined by comparing the ratio of the widths of the faces, dental archs and the teeth. The Chi-square test of independence between facial form, arch form and tooth form, was executed and the significance level determined. The results were as follows : 1. The distribution of facial forms was 66.1% square-tapering, 27.0% square, 5.2% ovoid, 2% tapering-square. 2. The distribution of tooth forms was 65.2% ovoid, 20.0% square-tapering, 11.3 % tapering-square, 3.5 % square. 3. The distribution of arch forms was 50.4 % square-tapering, 48.7 % tapering, 0.9 % reverse tapering-square. 4. There was no large differences in the distribution of facial forms, dental arch forms and tooth-forms between male and female. 5. No relationship existed between the tooth form and the facial form. 6. No relationship existed between the facial form and the dental arch form. 7. No relationship existed between the tooth form and the dental arch form. 8. This gave the impression that dental arch form and facial form could not be used as a true index in tooth selection.

• 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.

• Imaging Science in Dentistry
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• v.36 no.1
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• pp.17-24
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• 2006

Purpose : The objective of this study was to investigate the effect of TMJ disc displacement on the TMJ disc configuration and surrounding osseous structure. Materials and Methods : The proton density and 72-weighted MR images of 57 TMJs were retrospectively studied. These TMJs were divided into three groups according to the anterior disc displacement status on MR sagittal images, those were the normal, anterior disc displacement with reduction (ADWR), anterior disc displacement without reduction (ADWOR). The frequency of disc configuration and surrounding bony change, the border status between articular disc and retrodiscal tissue were investigated according to the positional change of articular disc. Results : There were significant statistical differences of chi-square statistics of TMJ disc configurational type between normal and ADWR/ADWOR group, respectively. Surrounding bony change frequently appeared in ADWOR and a statistically significant difference of chi-square statistics of bony change frequency between normal and ADWOR group was observed. Conclusion : These results suggested that the disc configuration and bony change of TMJ are strongly related to TMJ disc displacement.