• Communications of Mathematical Education
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• v.26 no.3
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• pp.251-271
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• 2012

The purpose of this study is: 1) to determine error sources and the effects of each error source, 2) to investigate optimal measuring conditions from holistic and analytic scoring methods, and 3) to compare the value of reliability between Cronbach's alpha and the generalizability coefficient in self-introduction letter and teacher's recommendation letter based on the generalizability theory in identification of mathematical gifted students by observations and nominations. Data of this study were collected from the science education institute for the gifted attached to the university located within in a capital city for the 2011 academic year. Scores form two raters using holistic and analytic scoring methods in both assessment types were used. The results of this study were as follows. First, as to both assessment types, error sources for people were relatively large regardless of scoring methods. However, error sources for raters in holistic scoring methods had a more significant impact than those of analytic scoring methods. Second, to set optimal measuring conditions in the self-introduction letter and teacher's recommendation letter, if we fixed the number of raters into 2 based on holistic scoring methods, at least 5 and 10 content domains were needed, respectively. In addition, the number of items in teacher's recommendation letter should be more than 3 when we fixed the number of content domains into 4, and the number of items in self-introduction letter should be more than 8 when we fixed the number of content domains into 6 using analytic scoring methods. Third, Cronbach's alpha having only a single source of errors was higher than the generalizability coefficient regardless of assessment types and scoring methods. Hence we recommend that generalizability coefficient based on various error sources such as raters, content domains, and items should be considered to keep a satisfactory level of reliability in both assessment types.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.775-791
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• 2017

We frequently encounter binary data in real life. Logistic, Probit, Cauchit, Complementary log-log models are often used for binary data analysis. In order to analyze binary data, Liu (2004) proposed a Robit model, in which the inverse of cdf of the Student's t distribution is used as a link function. Kim et al. (2008) also proposed a generalized t-link model to make the binary regression model more flexible. The more flexible skewed distributions allow more flexible link functions in generalized linear models. In the sense, we propose a binary data regression model using skewed generalized t distributions introduced in Theodossiou (1998). We implement R code of the proposed models using the glm function included in R base and R sgt package. We also analyze Pima Indian data using the proposed model in R.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.149-150
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• 2003

소표본 분할표 자료에서 적합도 검정통계량들의 카이제곱 근사 적용 가능에 대하여 많은 연구가 진행되었다. 소표본에서 세 가지 검정 통계량(피어슨 카이제곱 $X^{2}$, 일반화 가능도비 $G^{2}$, 그리고 역발산 I(2/3) 검정통계량)에 관하여 비교한 Rudas(1986)의 연구를 확장하여, 최근에 제안된 차이측도(BWHD(1/9), BWCS(1/3), NED(4/3) 검정통계량)를 포함시켜 비교 분석하였다. 독립모형의 이차원 분할표, 조건부 독립모형과 한 변수 독립 모형을 따르는 삼차원 분할표에 대한 모의실험을 통하여 생성된 90과 95 백분위수와 이에 대응하는 95% 신뢰구간을 살펴보고 실제 백분위수와 비교하였다. 그 결과 $X^{2}$, I(2/3), 그리고 BWHD(1/9) 검정통계량이 유사한 결과를 나타내었고 이 통계량들이 기존에 제안된 검정통계량들보다 적은 표본크기에서도 카이제곱 근사방법에 적용 가능함을 발견하였다.

• School Mathematics
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• v.6 no.4
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• pp.389-409
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• 2004

This article presents a case study in which three middle school students developed models in modeling activity using a tool. We research the interaction of model development process and the activities operating a tool in the modeling. And we investigate whether students are able to create generalizable model, after a tool mediates students' thought process and students internalize the perceptive activity operating a tool. The analysis of our case study led to three results. First, as students were able to integrate perceptive activity operating a tool and cognitive activity, they reasoned about the relationships among changing quantities and developed the model. Second, students corrected and refined developed models with reflecting the perceptive activity operating a tool. Third, as students internalized perceptive activity, students were able to create generalizable model, which is a graph of height as a function of the amount of water that's in the beaker.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.947-956
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• 2015

In the knowledge and information age, to discover and protect Intellectual Properties would be very important for their economic value as a major growth engine. This study evaluated the reliability of a Delphi survey conducted by experts to assess the value of agricultural resources knowledge obtained from literature reviews and field interviews. Delphi method is collecting the opinions of experts for several rounds repeatedly, in the next round the experts have chance to modify their opinion. Scores between two rounds are highly correlated and standard deviations are declined for second round to imply that some correction of their evaluations are made. To check reliability of Delphi survey of two rounds Cronbach's reliability coefficient and Generalizability coefficient are derived. The Cronbach alpha's supported the reliability of the method, but the Generalizability analysis revealed some unexpected results while checking the variance components of sources of measurement errors. Despite the increased reliability coefficients, the deviations between the raters are increased which means that additional rounds are required to get consensus, the goal of Delphi research.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.395-407
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• 2016

This study aims to apply the G-theory for estimation of reliability of evaluation scores between raters on Taekwondo Poomsae rating categories. Selecting a number of game days and raters as multiple error sources, we analyzed the error sources caused by relative magnitude of error variances of interaction between the factors and proceeded with D-study based on the results of G-study for optimal determination of measurement condition. The results showed below. The estimated outcomes of variance component for accuracy among the Taekwondo Poomsae categories with G-theory showed that impact of error was the biggest influence factor in raters conditions and in order of interaction in subjects and between subjects, also impact of variance component estimation error on expression category was the major influence factor in interaction and in order of the between subjects and raters. Finally, the result of generalizability coefficient estimation via D-study showed that measurement condition of optimal level depend on the number of raters was 8 persons of raters on accuracy category, and stable reliability on expression category was gained when the raters were 7 persons.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.5
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• pp.323-330
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• 2018

This study examined the fairness of the teaching aptitude and personality test assigned to pre-service engineering teachers in a graduate school of education based on measurement traits. For this study, we analyzed the teaching aptitude and personality test scores of 99 students enrolled in engineering education in a graduate school of education located in the Seoul metropolitan area from 2013 to 2017. The main results were as follows. First, the estimated variance due to residual was generally the highest, followed by nesting of items within domains, pre-service engineering teachers, interactions of pre-service engineering teachers with domains, domains, and occasions. Second, dependability coefficients were better indicators than Cronbach's because the latter may have been overestimated by applying the traditional reliability coefficient in inappropriate manners. Third, the teaching aptitude and personality test can be applied to pre-service engineering teachers in a graduate school of education based on empirical evidence considering dependability coefficients. Fourth, a total of 96 items from the original 210 items, with 2 occasions and 12 domains containing 8 items in each domain, were optimal measurement conditions to reach adequate degrees of reliability based on the total number of items. Finally, the results were discussed, the study limitations described and future research directions proposed.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.957-981
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• 2017

A generalized linear mixed model is an extension of a generalized linear model that allows random effect as well as provides flexibility in developing a suitable model when observations are correlated or when there are other underlying phenomena that contribute to resulting variability. We describe maximum likelihood estimation methods for logistic regression models that include random effects - the Laplace approximation, Gauss-Hermite quadrature, adaptive Gauss-Hermite quadrature, and pseudo-likelihood. Applications are provided with social science problems by analyzing the effect of mental health and life satisfaction on volunteer activities from Korean welfare panel data; in addition, we observe that the inclusion of random effects in the model leads to improved analyses with more reasonable inferences.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.10A
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• pp.962-968
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• 2002

Reliable high-speed data communications over insufficient channel bandwidth is one of the major challenges of harsh wireless environments that push the achievable spectral efficiency far below its theoretical limits. A Quadrature amplitude modulation (QAM) scheme is a userful modulation technique for achieving high data rate transmission without increasing the bandwidth of wireless communication systems. The exact general bit error rate (BER) expression of arbitrary rectangular quadrature amplitude modulation has not yet been derived. In this paper, a generalized closed-form expression for the BER performance of rectangular QAM with Gray code bit mapping is derived and analyzed in the presence of additive white Gaussian noise (AWGN) channel. First we analyze the BER performance of an I-ary PAM scheme. Regular patterns in the k-th bit error probability are observed while developing the EBR expression. From these patterns we provide the exact and general closed-from EBR expression of an I-ary PAM. Then we present a general closed-from expression for BER of an arbitrary IXJ rectangular QAM by considering that this signaling format consists of two PAM scheme, i.e., I-ary and J-ary PAM. A simple approximate BER expression for rectangular QAM is given as well.