• Communications for Statistical Applications and Methods
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• v.31 no.1
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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.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.10 no.4
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• pp.85-92
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• 2002

To investigate the safety of the in-use vehicles emission against the tail-pipe emission regulation, in-use vehicles emission trend according to vehicle mileage should be known. But it is impossible to collect all vehicles emission data In order to know that. Therefore, it is necessary to establish a statistically meaningful inference method that can be used generally to estimate in-use vehicles emissions distribution according to the vehicle mileage with relatively less in-use vehicles emission data. To do this, a linear regression model that solved the problems of data normality and common variance of error was studied. As a way that can secure the data normality, In(emission) instead of emission itself was used as a sampled data. And a reciprocal of mileage was suggested as a factor to secure common variance of error. As an example, 36 data of FTP-75 test were handled in this study. As a result, using average value and standard deviation at each mileage which were inferred from a linear regression model, probability density distribution and cumulative distribution of emissions according to the vehicle mileage were obtained and it was possible to predict the deterioration factor through full useful life mileage and also possible to decide whether those in-use vehicles will meet the tail-pipe emission regulations or not.

• Journal of Embryo Transfer
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• v.11 no.1
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• pp.27-33
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• 1996

The efficient cryopreservation of embryos requires optimal times of dehydration and rehydration This study was carried out to investigate the effect of various times of dehydration and rehydration The effects were evaluated through testing morphological normality and developmental ability of 1 cell mouse embryos which were ultrarapidly frozen and thawed. The 1 cell embryos were dehydrated for 1.5, 3, 5, and 10 minutes using mPBS-BSA containing 3.SM DMSO and 0.25M sucrose on cooling chamber or on ice. After ultrarapidly frozen and thawed, they were rehydrated for 0, 0.5 and 5 minutes with mPBS-BSA containing 0.25M sucrose at room temperature. The results obtained were as follows: The embryos that were rehydrated for 0.5 minutes showed higher normality than the embryos for 0 and 5 minutes did. The embryos that were dehydrated for 10 minutes showed higher normality than the embryos for 1.5, 3, and 5 minutes did. The developmental ability of normal thawed-embryos was high in 10 minute dehydration treatment compared to other treatments. However, it was not affected by cooling methods (on ice and on cooling chamber) for embryo dehydration.

• Journal of the Korean Mathematical Society
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• v.14 no.2
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• pp.217-221
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• 1978

• The Mathematical Education
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• v.11 no.2
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• pp.17-18
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• 1973

• Communications for Statistical Applications and Methods
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• v.19 no.4
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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.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.639-646
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• 2015

We propose simultaneous tests for mean and variance under the normality assumption. After formulating the null hypothesis and its alternative, we construct test statistics based on the individual p-values for the partial tests with combining functions and derive the null distributions for the combining functions. We then illustrate our procedure with industrial data and compare the efficiency among the combining functions with individual partial ones by obtaining empirical powers through a simulation study. A discussion then follows on the intersection-union test with a combining function and simultaneous confidence region as a simultaneous inference; in addition, we discuss weighted functions and applications to the statistical quality control. Finally we comment on nonparametric simultaneous tests.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.19-30
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• 2003

In this paper we present a new family of distributions that allows a continuous variation not only from normality to non-normality but also from unimodality to bimodality. Its properties are especially useful in studying and making inferences about models involving the univariate truncated normal distribution. The properties of the family and its applications are given.

• Journal of Physiology & Pathology in Korean Medicine
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• v.19 no.1
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• pp.289-293
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• 2005

The aim of this study was to investigate the importance of behavior habit and body exercise. We divided 164 volunteers into 2 groups. 82 volunteers was obese group($BMI{\geqq}25$), and the others was normal group(BMI<25). And we investigated the difference of water distribution and muscle circumference of arm, leg and trunk of between obese patient and normality. The results are as follows; Normal group was significantly higher than obese group in leg water distribution and muscle circumference rate as compared with arm(P<0.001). Normal group was significantly higher than obese group in leg water distribution and muscle circumference rate as compared with trunk(P<0.001). Each of the relation of water distribution and muscle circumference was significantly correlated with Pearson correlation analysis(r = 0.96, r = 0.6). In conclusion, there is very important that Low limb exercise and behavior habit in obese.