• Research in Mathematical Education
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• v.11 no.4
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• pp.275-283
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• 2007

In this study, we gave 132 high school students fifteen probabilities and nine statistics problems of the Korean College Scholastic Aptitude Test and then analyzed their answer using the classical test theory and the item response theory. Using the classical test theory (the Testian 1.0) we get the item reliability ($0.730 \sim 0.765$), and using the item response theory (the Bayesian 1.0) we get the item difficulty ( $-2.32\sim0.83$ ) and discrimination ( $0.55\sim 2.71$). From results, we find out what and why students could not understand well.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.363-381
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• 2012

Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ${\psi}$ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.107-124
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• 1999

An approximate Bayes criterion for multivariate Behrens-Fisher problem is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approach introduced by Speigelhalter and Smith (1982). The criterion is designed to develop a Bayesian test, so that it provides an alternative test to other tests based upon asymptotic sampling theory (such as the tests suggested by Bennett(1951), James(1954) and Yao(1965). For the derived criterion, numerical studies demonstrate routine application and give comparisons with the classical tests.

• The Korea Journal of Herbology
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• v.37 no.2
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• pp.13-21
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• 2022

Objectives : The evaluation of academic achievement is pivotal for establishing accurate direction and adequate level of medical education. The purpose of this study was to firstly establish innovative item analysis technique of Item Response Theory (IRT) for analyzing multiple-choice test of herbology in the traditional Korean medicine education which has not been available for the difficulty of test theory and statistical calculation. Methods : The answers of 390 students (2012-2018) to the 14 item herbology test in college of Korean medicine were used for the item analysis. As for the multidimensional analysis of item characteristics, difficulty, discrimination, and guessing parameters along with item-total correlation and percentage of correct answer were calculated using Classical Test Theory (CTT) and IRT. Results : The validity parameters of strong and weak items were illustrated in multiple perspectives. There were 4 items with six acceptable index scores, and 5 items with only one acceptable index score. The item discrimination of IRT was found to have no significant correlation with difficulty and discrimination indices of CTT emphasizing attention of professionals of medical education as for the test credibility. Conclusion : The critical suggestions for the development, utilization and revision of test items in the e-learning and evidence-based Teaching era were made based on the results of item analysis using IRT. The current study would firstly provide foundation for upgrading the quality of Korean medicine education using test theory.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.11 s.176
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• pp.210-217
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• 2005

A curl distortion induced by shrinkage during stereolithography polymerization process is analyzed with the classical lamination theory. Test parts of different layer thickness and part thickness are manufactured and their deformations are measured with CMM. Curl distortion is generated by the differential shrinkage of the layers, where the total shrinkage includes the shrinkages due to solidification and the change of temperature. It is shown that the curl distortion increases exponentially with decreasing the total thickness of the part, whose smaller layer thickness induces larger curl distortion. It is verified that only a part of the total shrinkage plays a role in generating the curl distortion.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.337-354
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• 2015

In this article, free vibration of functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been investigated. Literature review reveals no study has been performed based on functionally graded elliptic plates till date. The mechanical kinematic relations are considered based on classical plate theory. Rayleigh-Ritz technique is used to obtain the generalized eigenvalue problem. The material properties of the FG plate are assumed to vary along thickness direction of the constituents according to power-law form. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any edge support. The objective is to study the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. A comparison study is carried out with existing literature for validation in special cases. Three-dimensional mode shapes for circular and elliptic FG plates are also presented with various boundary conditions at the edges.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.473-485
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• 2017

An isolated building, composed of superstructure and isolation system which have very different damping properties, is typically non-classical damping system. This results in inapplicability of traditional response spectrum method for isolated buildings. A multidimensional response spectrum method based on complex mode superposition is herein introduced, which properly takes into account the non-classical damping feature in the structure and a new method is developed to estimate velocity spectra from the commonly used displacement or pseudo-acceleration spectra based on random vibration theory. The error of forced decoupling method, an approximated approach, is discussed in the viewpoint of energy transfer. From the base-isolated benchmark model, as a numerical example, application of the procedure is illustrated companying with comparison study of time-history method, forced decoupling method and the proposed method. The results show that the proposed method is valid, while forced decoupling approach can't reflect the characteristics of isolated buildings and may lead to insecurity of structures.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.193-205
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• 1999

An approximate Bayes criterion for Behrens-Fisher problem (testing equality of means of two normal populations with unequal variances) is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approachintroduced by Spiegelhalter and Smith (1982). The proposed criterion is designed to develop a Bayesian test criterion having a closed form, so that it provides an alternative test to those based upon asymptotic sampling theory (such as Welch's t test). For the suggested Bayes criterion, numerical study gives comparisons with a couple of asymptotic classical test criteria.

• Journal of Korean Biological Nursing Science
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• v.20 no.1
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• pp.11-19
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• 2018

Purpose: The purposes of this study were to perform items analysis using the classical test theory (CTT) and the item response theory (IRT), and to establish the validity and reliability of the Korean version of pressure ulcer prevention knowledge. Methods: The 26-item pressure ulcer prevention knowledge instrument was translated into Korean, and the item analysis of the 22 items having an adequate content validity index (CVI), was conducted. A total of 240 registered nurses in 2 university hospitals completed the questionnaire. Each item was analyzed applying CTT and IRT according to 2-parameter logistic model. Response alternatives quality, item difficulty and item discrimination were evaluated. For testing validity and reliability, Pearson correlation coefficient and Kuder Richardson-20 (KR-20) were used. Results: Scale CVI was .90 (Item-CVI range= .75-1.00). The total correct answer rate for this study population was relatively low as 52.5%. The quality of response alternatives was found to be relatively good (range= .02-.83). The item difficulty of the questions ranged form .10 to .86 according to CTT and -12.19 to 29.92 according to the IRT. This instrument had 12-low, 2-medium and 8-high item difficulty applying IRT. The values for the item discrimination ranged .04-.57 applying CTT and .00-1.47 applying IRT. And overall internal consistency (KR-20) was .62 and stability (test-retest) was .82. Conclusion: The instrument had relatively weak construct validity, item discrimination according to the IRT. Therefore, the cautious usage of a Korean version of this instrument would be recommended for discrimination because there are so many attractive response alternatives and low internal consistency.