• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.851-858
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• 2001

Using the normalized sample Lorenz curve which is introduced by Kang and Cho (2001), we propose the test statistics for testing of normality that is very important test in statistical analysis and compare the proposed test with the other tests in terms of the power of test through by Monte Carlo method. The proposed test is more power than the other tests except some cases

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1664-1675
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• 2021

In order to verify the statistical performance of the nonparametric tests used in the MARSSIM approach, all plausible contamination distribution types that can be encountered in a survey area should be investigated. As the first of such investigations, this study aims to perform the verification for normal distribution of the contamination in a survey area by simulating the collection of random samples from it through the Monte Carlo simulation. The results of the simulations conducted for a total of 81 simulation cases showed that Sign test and WRS test both exhibited an excellent statistical performance: 100% for the former and 98.8% for the latter. Therefore, in final status surveys of the MARSSIM approach, a high statistical performance can be expected in applying the nonparametric hypothesis tests to survey areas whose net contamination can be assumed to be normally distributed.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.463-475
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• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.467-476
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• 1997

The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.453-465
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• 1997

The family of power-divergence statistics conditional on margins is considered for testing homogeneity of .tau. multinomial populations with equal sample size and the exact Bahadur slope is obtained. It is shown that the likelihood ratio test conditional on margins is the most Bahadur efficient among the family of power-divergence statistics.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.109-117
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• 2023

Intuitively, a test with more assumptions has greater power than a test with fewer assumptions. This kind of examples are abundant in the nonparametric tests vs corresponding parametric ones. In general, the nonparametric tests are less efficient in terms of asymptotic relative efficiency (ARE) compared to corresponding parametric tests (Daniel, 1990). However, this is not always true. To test equal means under independent normal samples, the usual test involves using the t-distribution with the pooled estimator of the common variance. Adding the assumption of equal sample size, we may derive another test. In this case, two tests using more assumptions were performed for univariate (multivariate) cases. For these examples, it was found that the power function of a test with more assumptions is less than or equal to that of a test with fewer assumptions. This finding can be used as an expository example in master's mathematical statistics courses.

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.309-316
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• 2014

Testing normality is very important because the most common assumption is normality in statistical analysis. We propose a new plot and test statistic to goodness-of-fit test for normality based on the generalized Lorenz curve. We compare the new plot with the Q-Q plot. We also compare the new test statistic with the Kolmogorov-Smirnov (KS), Cramer-von Mises (CVM), Anderson-Darling (AD), Shapiro-Francia (SF), and Shapiro-Wilks (W) test statistic in terms of the power of the test through by Monte Carlo method. As a result, new plot is clearly classified normality and non-normality than Q-Q plot; in addition, the new test statistic is more powerful than the other test statistics for asymmetrical distribution. We check the proposed test statistic and plot using Hodgkin's disease data.

• Korean Journal of Veterinary Research
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• v.48 no.3
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• pp.357-361
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• 2008

Although power analysis is of important tool of research, investigators in veterinary medicine are unaware of the concepts of the statistical power. Two types of error occur in classical hypothesis testing and, those errors should be avoided, if possible. Since power is highly dependent on the sample size, whenever declaring non-statistically significant result they should consider the potential for committing a Type II error in their studies, which refers to the probability of falsely stating that two treatments are equivalent despite true difference between them. Also, sample size determination is one of the most important tasks facing the researcher when planning a diagnostic study, and provides valuable information on the characteristics of a test performance. This type of analysis forms the basis for proper interpretation of test results. The aim of this article was to re-evaluate some selected studies on diagnostic test reported in the domestic veterinary publications to determine the power and necessary sample size for inequality testing to ensure the desired power. Power calculations were illustrated using real-life examples of comparison of a new test and a reference test for detecting antibodies of various animal diseases. Factors affecting to the power were also discussed.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.423-435
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• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.139-149
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• 1997

For split plot designs exact univariate F tests of the within-subjects main effect are based on the assumption of multisample sphericity. Type I error rates and power are reported for the F test and two tests designed for use when multisample sphericity is violated: the $\widetilde{\xi}$-adjusted test and the Corrected Improved General Approximation(CIGA) test.The results indicate that even though the F test and the $\widetilde{\xi}$-adjusted test have better power than the CIGA test in some conditions, the F test and the $\widetilde{\xi}$-adjusted test do not control Type I error rates when the design is unbalanced and the F test dose not have a good control of Type I error rates when sphericity assumption is severely violated.