• The Mathematical Education
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• v.41 no.1
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• pp.109-126
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• 2002

In this thesis. we estimated the good reliability coefficient ${\beta}$$\sub$k/ that is unbiased, consistent and more efficient than Cronbach's ${\alpha}$$\sub$k/ in splitting of a test into several formats of subtests and several properties of ${\beta}$$\sub$k/ are also represented. The tables of coefficients of skewness and kurtosis are represented to test the significance of departures from normality. We got the cumulative normal plots of z'from the distribution which is departed from normality using the Bock's approximation procedure and we finally enumerated the transformed standardized scores z'and a new raw score X' which enable us to proceed further evaluation procedures depending on our assessment policy.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.223-232
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• 2002

The present paper develops a test of the multivariate normality based on nonlinear transformations and the likelihood function. For checking the normality, we test the shape parameter which indexes the family of transformations. A score test and a parametric bootstrap test are used to evaluate the discrepancy between the data and a multivariate normal distribution. In order to compare the performance of our test with the existing tests, a simulation study was carried out for several situations where nuisance parameters have to be estimated. The results showed that the proposed method is superior to the existing methods.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.119-129
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• 2003

We propose a new logistic regression model of normality curves for normal(diseased) and abnormal(nondiseased) classifications by neural networks in data mining. The fitted logistic regression lines are estimated, interpreted and plotted by the neural network technique. A few goodness-of-fit test statistics for normality are discussed and the performances by the fitted logistic regression lines are conducted.

• Journal of Korean Society on Water Environment
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• v.21 no.6
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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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• v.6 no.3
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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.

• International Journal of Reliability and Applications
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• v.1 no.2
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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.

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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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.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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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.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.429-436
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• 1999

We suggest test statistics for normality using Q-Q plot and P-P plot and obtain empirical quantities of these statistics. Also the power comparison with Shapiro-Wilk's W is conducted by Monte Carlo study.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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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.