• Communications for Statistical Applications and Methods
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• v.9 no.2
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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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• v.36 no.3
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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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• v.17 no.3
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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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• v.7 no.2
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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.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.377-393
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• 2003

Several confidence interval estimates for the difference of two binomial proportions were introduced. Bootstrap confidence interval is also suggested. We examined the over estimation property of approximate intervals and under estimation trend of exact intervals for the difference of proportions. We compared these confidence intervals based on the average coverage probability, expected width and skewness measure. Particularly actual coverage probability were calculated by using the prior distribution of parameters. Monte Carlo simulation for small sample size is conducted. Some interesting contour plots of average coverage probability and marginal plots for several interval estimates are presented.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.793-804
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• 2009

The hypotheses of difference, ratio and odds ratio between two proportions are used for the non-inferiority trial. The approximate unconditional test suggested by Kang and Chen (2000) based on difference and ratio have the potential problem against the failure rate. When the sample size is small, the type I errors of the asymptotic test using the normal approximation suggested by Chen et al. (2000) tends to exceed the nominal level. Therefore, we propose the approximate unconditional test based on odds ratio and compare the test with the asymptotic test. And we compare the three hypotheses used in the approximate unconditional tests of two proportions with respect to the type I errors and power.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.169-179
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• 2003

We suggest two types of misuses to analyze the same survey data. One is related with the fact that people nay use the wrong bounds of error when they compare two proportions. And the other is related with that some non-statisticians are apt to use wrong methods when there is a neutral answer in a question. We suggest these methods and compare them with the statistically good method. It will be a good results in educational purpose.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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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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• v.17 no.5
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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.