• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.117-126
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• 2001

We provide a simple chi-squared test of multivariate normality based on rectangular cells on the spherical data. This test is simple since it is a direct extension of the univariate chi-squared test to multivariate case and the expected cell counts are easily computed. We derive the limiting distribution of the chi-squared statistic via the conditional limit theorems. We study the accuracy in finite samples of the limiting distribution and then compare the poser of our test with those of other popular tests in an application to a real data.

• Communications for Statistical Applications and Methods
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• 제27권5호
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• pp.501-510
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• 2020

Mardia (Biometrika, 57, 519-530, 1970) defined measures of multivariate skewness and kurtosis. Based on these measures, omnibus test statistics of multivariate normality are proposed using normalizing transformations. The transformations we consider are normal approximation and a Wilson-Hilferty transformation. The normalizing transformation proposed by Enomoto et al. (Communications in Statistics-Simulation and Computation, 49, 684-698, 2019) for the Mardia's kurtosis is also considered. A comparison of power is conducted by a simulation study. As a result, sum of squares of the normal approximation to the Mardia's skewness and the Enomoto's normalizing transformation to the Mardia's kurtosis seems to have relatively good power over the alternatives that are considered.

• Communications for Statistical Applications and Methods
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• 제21권6호
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• pp.539-559
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• 2014

We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.309-318
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• 2006

There are many statistical methods of testing the equality of two population variances. Among them, the well-known F test is very sensitive to the normality assumption. Several other tests that do not assume normality have been proposed, but these tests usually need tables of critical values or software for hypotheses testing. McGrath and Yeh (2005) suggested a quick and compact Count Five test requiring only the calculation of the number of extreme points. Since the Count Five test uses only extreme values, this discards some information from the samples, often resulting in a degradation in power. In this paper, an alternative Count Five test using the trimmed mean is proposed and its properties are discussed for some distributions and normal mixtures.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제44권1호
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• pp.25-28
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• 2018

Objectives: This study aimed to describe recent patterns in the types of statistical test used in original articles that were published in Journal of the Korean Association of Oral and Maxillofacial Surgeons. Materials and Methods: Thirty-six original articles published in the Journal in 2015 and 2016 were ascertained. The type of statistical test was identified by one researcher. Descriptive statistics, such as frequency, rank, and proportion, were calculated. Graphical statistics, such as a histogram, were constructed to reveal the overall utilization pattern of statistical test types. Results: Twenty-two types of statistical test were used. Statistical test type was not reported in four original articles and classified as unclear in 5%. The four most frequently used statistical tests constituted 47% of the total tests and these were the chi-square test, Student's t-test, Fisher's exact test, and Mann-Whitney test in descending order. Regression models, such as the Cox proportional hazard model and multiple logistic regression to adjust for potential confounding variables, were used in only 6% of the studies. Normality tests, including the Kolmogorov-Smirnov test, Levene test, Shapiro-Wilk test, and $Scheff{\acute{e}}^{\prime}s$ test, were used diversely but in only 10% of the studies. Conclusion: A total of 22 statistical tests were identified, with four tests occupying almost half of the results. Adoption of a nonparametric test is recommended when the status of normality is vague. Adjustment for confounding variables should be pursued using a multiple regression model when the number of potential confounding variables is numerous.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2008년도 춘계학술대회
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• pp.295-299
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• 2008

This paper discusses tests of factor effect or contrast by the use of saturated design $k^n$ factorial design. The nine nonparametric rank measures in normality test using normal probability pot are proposed. Length's PSE(Pseduo Standard Error) test [4] which relies on the concept of effect sparsity is also introduced and extended to the margin of error(ME) and Simultaneous margin of error(SME).

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.57-65
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• 1999

In a resent paper, Na, Lee and Kim(1998) develop a test statistic for testing whether or not the mean residual life changes its trend based on complete data and show that the new test performs better than previously known tests. In this paper, we extend their test to the randomly censored data. The asymptotic normality of the test statistic is established. Monte Carlo simulations are conducted to compare our test with a previously known test by the power of tests.

• 대한산업공학회지
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• 제10권2호
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• pp.51-65
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• 1984

A process quality control system is designed which incorporates run tests, normality test, process capability studies, etc., into control chart scheme, and a software package for microcomputers is developed. The system is interactive and has data base management capabilities. All programs are written in BASIC language.

• 응용통계연구
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• 제15권2호
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• pp.223-232
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• 2002

이 논문에서는 비선형 변환과 가능도 함수를 이용하여 다변량 자료의 정규성을 검정하는 방법에 대해 알아본다. 사용된 변환은 변환모수에 따라 여러 가지 형태를 가지는 변환족을 구성하는데 이 변환모수를 검정하여 자료의 정규성을 검정한다. 모수의 검정은 점수함수(score function)을 기초로 이루어지며 표본크기가 적은 경우에도 검정통계량의 분포를 유도하기 위한 모수적 붓스트랩 검정방법이 사용된다. 모의실험 결과 기존의 방법과 검정력을 비교하여 제안된 방법이 검정력이 높은 것으로 나타났다.

• Communications for Statistical Applications and Methods
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• 제25권4호
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• pp.329-339
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• 2018

In this study, we propose tests for equality of several variances with the normality assumption. First of all, we propose the likelihood ratio test by applying the permutation principle. Then by using the p-values for the pairwise tests between variances and combination functions, we propose combination tests. We apply the permutation principle to obtain the overall p-values. Also we review the well- known test statistics for the completion of our discussion and modify a statistic with the p-values. Then we illustrate proposed tests by numerical and simulated data and compare their efficiency with the reviewed ones through a simulation study by obtaining empirical p-values. Finally, we discuss some interesting features related to the resampling methods and tests for equality among several variances.