• 한국물환경학회지
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• 제21권6호
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• pp.651-658
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• 2005

The Non-parametric Analysis is powerful in data test especially for the non- normality water quality data. The data at three monitoring stations of the Tam-Jin River were evaluated for their normality using Skewness, Q-Q plot and Shapiro-Willks tests. Various constituent of water quality data including temperature, pH, DO, SS, BOD, COD, TN and TP in the period of January 1994 to December 2004 were used as dataset. Shapiro-Willks normality test was carried out for a test 5% significance level. Most water quality data except DO at monitoring stations 1 and 2 showed that data does not normally distributed. It is indicating that non-parametric method must be used for a water quality data. Therefore, a homogeneity was conducted by Mann-Whitney U test (p<0.05). Two stations were paired in three pairs of such stations. Differences between stations 1, 2 and stations 1, 3 for pH, BOD, COD, TN and TP were meaningful, but Tam-Jin 2 and 3 stations did not meaningful. In addition, a narrow gap of the water quality ranges is not a difference. Categories in which all three pairs of stations (1 and 2, 2 and 3, 1 and 3) in the Tam-Jin River showed difference in water quality were analyzed on TN and TP. The results of in this research suggest a right analysis in the homogeneity test of water quality data and a reasonable management of pollutant sources.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.687-694
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• 1999

The goodness of fit statistics of normality plots are obtained using the Receiver Operating Characteristic(ROC) method. This work is intended to compare with Shapiro-Wilk W statistic. Wel will use and discuss an accuracy of the test and the best cut-off value which minimizes the sum of the type I and II error probabilities.

• 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.

• 응용통계연구
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• 제17권1호
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• pp.35-47
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• 2004

본 논문에서는 Kim & Bickel(2003)에서 제안한 이변량 정규분포를 위한 검정통계량을 Fattorini(1986)의 방법을 이용하여 이변량 이상인 경우에도 실제적으로 사용가능 하도록 일반화하였다. Fattorini(1986)의 통계량은 Shapiro & Wilk(1965)의 일변량 정규분포를 위한 검정통계량을 다변량으로 확장한 것이다. 그리고 제안된 통계량은 Fat-torini(1986) 통계량의 근사통계량으로 생각할 수 있으며 표본의 크기가 클 때도 사용 가능하다. 또한 모의실험을 통하여 여러 가지 대립가설에서 기존의 통계량과의 검정력을 비교하였다.

• 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.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2012년 춘계학술대회
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• pp.579-583
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• 2012

The Design of Experiment (DOE) is a most practical technique when establishing an optimal condition for production technology in Six Sigma innovation project. This research proposes the assessment of properties of error terms, such as normality, equal variance, unbiasedness and independence. The properties of six nonparametric ranking techniques for checking normality assumption are discussed as well as run test which is used to identify the randomness, and to check unbiased assumption. Furthermore, Durbin-Watson (DW) statistics and ARIMA (p,d,q) process are discussed to identify the serial correlation.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.429-436
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• 1999

정규분포에 관한 검정에 있어서 P-P 플롯과 Q-Q 플롯에서 정규분포에서의 기대 직선의 잔차들을 이용한 두 가지 통계량을 제시하고, 이 통계량들의 경험적 분위수(empirical quantile)를 구하였다. 그리고 이들 통계량의 검정력을 Shapiro-Wilk의 W 통계량과의 비교를 통하여 분석하였다.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.1-35
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• 2024

The assumption of homoscedasticity is one of the most crucial assumptions for many parametric tests used in the biological sciences. The aim of this paper is to compare the empirical probability of type I error and the power of ten parametric and two non-parametric tests for homoscedasticity with simulations under different types of distributions, number of groups, number of samples per group, variance ratio and significance levels, as well as through empirical data from an agricultural experiment. According to the findings of the simulation study, when there is no violation of the assumption of normality and the groups have equal variances and equal number of samples, the Bhandary-Dai, Cochran's C, Hartley's Fmax, Levene (trimmed mean) and Bartlett tests are considered robust. The Levene (absolute and square deviations) tests show a high probability of type I error in a small number of samples, which increases as the number of groups rises. When data groups display a nonnormal distribution, researchers should utilize the Levene (trimmed mean), O'Brien and Brown-Forsythe tests. On the other hand, if the assumption of normality is not violated but diagnostic plots indicate unequal variances between groups, researchers are advised to use the Bartlett, Z-variance, Bhandary-Dai and Levene (trimmed mean) tests. Assessing the tests being considered, the test that stands out as the most well-rounded choice is the Levene's test (trimmed mean), which provides satisfactory type I error control and relatively high power. According to the findings of the study and for the scenarios considered, the two non-parametric tests are not recommended. In conclusion, it is suggested to initially check for normality and consider the number of samples per group before choosing the most appropriate test for homoscedasticity.

• International Journal of Reliability and Applications
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• 제1권2호
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• pp.115-121
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• 2000

The trend change in aging properties, such as failure rate and mean residual life, of a life distribution is important to engineers and reliability analysts. In this paper we develop a test statistic for testing whether or not the failure rate changes its trend using censored data. The asymptotic normality of the test statistics is established. We discuss the efficiency values of loss due to censoring.

• Communications for Statistical Applications and Methods
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• 제19권4호
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• pp.607-617
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• 2012

The goodness-of-fit test for multivariate normal distribution is important because most multivariate statistical methods are based on the assumption of multivariate normality. We propose goodness-of-fit test statistics for multivariate normality based on the modified squared distance. The empirical percentage points of the null distribution of the proposed statistics are presented via numerical simulations. We compare performance of several test statistics through a Monte Carlo simulation.