• Proceedings of the Safety Management and Science Conference
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• 2008.04a
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• pp.451-460
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• 2008

This paper reviews nonparametric statistics by Neyman-Pearson test and Fisher test. Nonparametric statistics deal with the small sample with distribution-free assumption in multi-product and small-volume production. Two tests for various nonparametric statistic methods such as sign test, Wilcoxon test, Mann-Whitney test, Kruskal-Wallis test, Mood test, Friedman test and run test are also presented with the steps for testing hypotheses and test of significance.

• Communications for Statistical Applications and Methods
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• v.17 no.1
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• pp.79-88
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• 2010

Introductory statistic class proposes two tests for the equality of two population means according to the homogeneity of their variances. However, in practice, the variances are also unknown and practitioners often test their homogeneity before they do two sample t-test. This is also true in many popular statistical packages such as SAS and SPSS. In this paper, we study the type I error of this two stage procedure and propose a procedure to control it at a given significance level.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.135-149
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• 1994

We discussed a comparison of distribution-free two-sample procedures based on placements or ranks. Iterative asymptotic distribution of both two-sample procedures is studies and small sample Monte Carlo simulation results are presented. Also, we proposed the Hodges-Lehmann type location estimator based on linear placement statistics.

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.339-352
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• 1997

Chi-square test based on large sample theory is inappropriate for testing the row homogeneity in two-way contingency table with several sparse cells. For that case, exact testing methods has been developed in the literature and implemented in StatXact(1991). However, considerable computing time is inevitable for moderate size tables. So, Monte Carlo approximation is recommended frequently. In this study, we propose a simple algorithm for generating two-way random tables with fixed row and column margins for small sample chi-square test. Also, we develop “Turkey-type” method for multiple between-row comparisons.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.377-383
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• 2003

In this paper, we consider two components system in which the lifetimes follow the bivariate Pareto model with random censored data. We assume that the censoring time is independent of the lifetimes of the two components. We develop large sample tests for testing independence between two components. Also we present simulated study which is the test based on asymptotic normal distribution in testing independence.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.83-90
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• 2000

The chi-squared test statistic is usually employed for testing independence of two categorical variables in a two-way contingency table. It is well known that, under independence, the test statistic has an asymptotic chi-squared distribution under multinomial or product-multinomial models. For the case where both margins fixed, the sampling model of the contingency table is a multiple hypergeometric distribution and the chi-squared test statistic follows the same limiting distribution. In this paper, we study the difference between the small sample and large sample distributions of the chi-squared test statistic for the case with fixed margins. For a few small sample cases, the exact small sample distribution of the test statistic is directly computed. For a few large sample sizes, the small sample distribution of the statistic is generated via a Monte Carlo algorithm, and then is compared with the large sample distribution via chi-squared probability plots and Kolmogorov-Smirnov tests.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1243-1251
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• 2010

For clinical trials, it is common to compare the placebo and new drug. The method of calculating a sample size for two independent populations are the t-test that is used for parametric methods, and the Wilcoxon rank-sum test that is used in the non-parametric methods. In this paper, we propose a method that is using Kim's (1994) statistic power based on the linear placement statistic, which was proposed by Orban and Wolfe (1982). We also compare the sample size for the proposed method with that for using Wang et al. (2003)'s sample size formula which is based on Wilcoxon rank-sum test, and with that of t-test for parametric methods.

• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1249-1263
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• 2009

The power function in sample size determination has to be characterized by an appropriate statistical test for the hypothesis of interest. Nonparametric tests are suitable in the analysis of ordinal data or frequency data with ordered categories which appear frequently in the biomedical research literature. In this paper, we study sample size calculation methods for the Wilcoxon-Mann-Whitney test for one- and two-dimensional ordinal outcomes. While the sample size formula for the univariate outcome which is based on the variances of the test statistic under both null and alternative hypothesis perform well, this formula requires additional information on probability estimates that appear in the variance of the test statistic under alternative hypothesis, and the values of these probabilities are generally unknown. We study the advantages and disadvantages of different sample size formulas with simulations. Sample sizes are calculated for the two-dimensional ordinal outcomes of efficacy and safety, for which bivariate Wilcoxon-Mann-Whitney test is appropriate than the multivariate parametric test.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.185-192
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• 2001

Using the Lorenz curve that is proved to be a powerful tool to measure the income inequality within a population of income receivers, we propose the normalized sample Lorenz curve for the goodness-of-fit test that is very important test in statistical analysis. For two hodgkin's disease data sets, we compare the Q-Q plot and the proposed normalized sample Lorenz curve.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.659-666
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• 1999

In comparing two population means, the test statistic depends on the sample means and the variances, which are very sensitive to the extremely large or small values. This paper aims at examining the behavior of such observations using proper criterion which can measure the influence of them. We derive a computationally feasible statistic which can detect influential observations on the two-sample t-statistic.