• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.389-399
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• 2002

In order to examine whether the difference between two point estimates of population proportions is statistically significant, data analysts use two techniques. The first is to explore the overlap between two associated confidence intervals. Second method is to test the significance which is introduced at most statistical textbooks under the common assumptions of consistency, asymptotic normality, and asymptotic independence of the estimates. Under the null hypothesis which is two population proportions are equal, the pooled estimator of population proportion is preferred as a point estimator since two independent random samples are considered to be collected from one population. Hence as an alternative method, we could obtain another confidence interval of the difference of the population proportions with using the pooled estimate. We conclude that, among three methods, the overlapped method is under-estimated, and the difference of the population proportions method is over-estimated on the basis of the proposed method.

• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.397-410
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• 2007

For the two groups data from multivariate binomial distribution, we consider a bootstrap approach to inferring the simultaneous confidence level and its standard error of a collection of the dependent confidence intervals for the difference of proportions with an experimentwise error rate at the a level are presented. The bootstrap method is used to estimate the simultaneous confidence probability for the difference of proportions.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.309-318
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• 2010

The construction of asymptotic confidence intervals is considered for the difference of binomial proportions in two doubly sampled data subject to false-positive error. The coverage behaviors of several likelihood based confidence intervals and a Bayesian confidence interval are examined. It is shown that a hierarchical Bayesian approach gives a confidence interval with good frequentist properties. Confidence interval based on the Rao score is also shown to have good performance in terms of coverage probability. However, the Wald confidence interval covers true value less often than nominal level.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.481-487
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• 2000

When we construct an interval estimate of two independent proportions with rare events, the standard approach based on the normal approximation behaves badly in many cases. The problem becomes more severe when no success observations are observed on both groups. In this paper, we compare two alternative methods of constructing a confidence interval of the difference of two independent proportions by use of simulation. One is based on the profile likelihood and the other is the Bayesian probability interval. It is shown in this paper that the Bayesian interval estimator is easy to be implemented and performs almost identical to the best frequentist's method -the profile likelihood approach.

• 응용통계연구
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• 제16권2호
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• pp.377-393
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• 2003

본 논문에서는 두 모비율의 차에 대한 기존의 신뢰구간들을 소개하고 붓스트랩 신뢰구간도 제안하였다 또한 모비율의 차에 대한 신뢰구간이 가지는 성질로서 근사신뢰구간의 하향추정의 문제와 정확신뢰구간의 상향추정의 문제점들을 확인하였고 평균포함 확률, 구간기대폭 그리고 왜도성 측면에서 종합적인 비교를 하였다. 특히 모수에 대한 사전분포를 가정하여 여러 신뢰구간들이 지니는 특징도 살펴보았다 기존의 신뢰구간들과 제안된 붓스트랩 신뢰구간은 소표본의 모의실험을 통하여 실제 포함확률의 평균을 기준으로 비교되었고 이항분포에서와 같이 정확신뢰구간이 지니는 보수성을 확인할 수 있었다. 신뢰구간의 평균포함확률의 등고선 그림도 소개하였다.

• 응용통계연구
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• 제22권4호
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• pp.793-804
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• 2009

두 모비율의 비열등성 시험의 가설에는 두 비율의 차(difference), 비(ratio) 그리고 오즈비(odds ratio)를 이용할 수 있다. Kang과 Chen (2000)이 제안한 두 치료율의 차에 대한 근사 무조건적 검정(Approximate Unconditional test)과 두 치료율의 비에 대한 검정은 실패율을 고려하지 않았으므로 귀무가설이 기각되었을 때 치료율이 비열등하다고 주장할 수 있으나 실패율도 비열등하다고 주장하기에는 문제의 여지가 있다. 오즈비에 대한 검정으로 Chen 등(2000)이 제안한 접근적 검정(Asymptotic test)은 대표본 이론에 근거하여 검정하기 때문에 소표본에서 제 1종의 오류를 범할 확률이 유의수준보다 클 수 있다. 이러한 단점을 보완하기 위해 본 논문에서는 기존의 오즈비 가설에 대한 점근적 검정에 기초하여 근사 무조건적 검정을 제안하였다. 또한 점근적 검정과의 검정력을 비교하고, 근사 무조건적 검정에서 세 가설 간에 검정력을 비교하였다.

• 응용통계연구
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• 제25권3호
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• pp.513-520
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• 2012

An Agresti-Coull type test is considered for the difference of binomial proportions in two doubly sampled data subject to false-positive error. The performance of the test is compared with the likelihood-based tests. It is shown that the Agresti-Coull test has many desirable properties in that it can approximate the nominal significance level with compatible power performance.

• 응용통계연구
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• 제16권1호
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• pp.169-179
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• 2003

동일조사에서 통계분석 자가 흔히 범하는 오류 두 가지를 제시하였다. 하나는 일반적인 조사에서 발표된 조사결과로부터 두 비율의 비교를 시도할 때 범하기 쉬운 오류이고, 다른 하나는 중립적 응답 항목이 있을 때 통계전문가가 아닌 사람들 가운데에서 범하기 쉬운 잘못이다. 이런 오류들을 제시하고, 통계적으로 정확한 방법과 비교하여 잘못 사용하는 방법들이 갖는 문제들을 보여 줌으로써 교육 자료로 활용할 수 있도록 했다.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.363-372
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• 2009

The difference of two independent binomial proportions is frequently of interest in biomedical research. The interval estimation may be an important tool for the inferential problem. Many confidence intervals have been proposed. They can be classified into the class of exact confidence intervals or the class of approximate confidence intervals. Ore may prefer exact confidence interval s in that they guarantee the minimum coverage probability greater than the nominal confidence level. However, someone, for example Agresti and Coull (1998) claims that "approximation is better than exact." It seems that when sample size is large, the approximate interval is more preferable to the exact interval. However, the choice is not clear when sample, size is small. In this note, an exact confidence and an approximate confidence interval, which were recommended by Santner et al. (2007) and Lee (2006b), respectively, are compared in terms of the coverage probability and the expected length.

• Communications for Statistical Applications and Methods
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• 제17권5호
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• pp.679-688
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• 2010

Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.