• 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.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1399-1412
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• 2016

We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.

• Nuclear Engineering and Technology
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• v.45 no.2
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• pp.151-164
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• 2013

A key input for the assessment of Human Error Probabilities (HEPs) with Human Reliability Analysis (HRA) methods is the evaluation of the factors influencing the human performance (often referred to as Performance Shaping Factors, PSFs). In general, the definition of these factors and the supporting guidance are such that their evaluation involves significant subjectivity. This affects the repeatability of HRA results as well as the collection of HRA data for model construction and verification. In this context, the present paper considers the TAsk COMplexity (TACOM) measure, developed by one of the authors to quantify the complexity of procedure-guided tasks (by the operating crew of nuclear power plants in emergency situations), and evaluates its use to represent (objectively and quantitatively) task complexity issues relevant to HRA methods. In particular, TACOM scores are calculated for five Human Failure Events (HFEs) for which empirical evidence on the HEPs (albeit with large uncertainty) and influencing factors are available - from the International HRA Empirical Study. The empirical evaluation has shown promising results. The TACOM score increases as the empirical HEP of the selected HFEs increases. Except for one case, TACOM scores are well distinguished if related to different difficulty categories (e.g., "easy" vs. "somewhat difficult"), while values corresponding to tasks within the same category are very close. Despite some important limitations related to the small number of HFEs investigated and the large uncertainty in their HEPs, this paper presents one of few attempts to empirically study the effect of a performance shaping factor on the human error probability. This type of study is important to enhance the empirical basis of HRA methods, to make sure that 1) the definitions of the PSFs cover the influences important for HRA (i.e., influencing the error probability), and 2) the quantitative relationships among PSFs and error probability are adequately represented.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.319-324
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• 2003

본 논문에서는 matched-pair design에서의 두 처리간 동등성/ 비열등성 검정에 대해 고려하였다. 기존에 비율차이나 risk ratio관점에서 동등성/비열등성 검정을 시행한 것과는 달리, 본 논문에서는 odds ratio에 기초하여 두 가지 검정통계량을 유도하였다. (1) constrained maximum likelihood estimator(mle)를 이용한 fieller type 통계량 (2) 제약없이 구한 mle를 사용한 wald-type 통계량). 비율 차이나 risk ratio에 기초한 기존의 통계적 방법들(비율차이에 근거한 (3) score-type 통계량과 (4) wald-type 통계량, risk ratio에 기초한 (5) fieller-type 통계량과 (6) wald-type 통계량)과 본 논문에서 제시한 두가지 통계량의 성능을 비교하기 위해 모의실험을 시행하였다. 모의실험 결과, 본 논문에서 제안한 constrained mle를 사용한 fieller type 통계량은 empirical type I error 측면에서 매우 만족스러운 결과를 보이고 있으며, 특히 비대각 셀의 확률이 작아질 경우에도 안정적인 성능을 보여준다.

• 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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.19 no.1
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• pp.4279-4295
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• 1977

Two types of model were established in order to product the soil moisture content by which information on irrigation could be obtained. Model-I was to represent the soil moisture depletion and was established based on the concept of water balance in a given soil profile. Model-II was a mathematical model derived from the analysis of soil moisture variation curves which were drawn from the observed data. In establishing the Model-I, the method and procedure to estimate parameters for the determination of the variables such as evapotranspirations, effective rainfalls, and drainage amounts were discussed. Empirical equations representing soil moisture variation curves were derived from the observed data as the Model-II. The procedure for forecasting timing and amounts of irrigation under the given soil moisture content was discussed. The established models were checked by comparing the observed data with those predicted by the model. Obtained results are summarized as follows: 1. As a water balance model of a given soil profile, the soil moisture depletion D, could be represented as the equation(2). 2. Among the various empirical formulae for potential evapotranspiration (Etp), Penman's formula was best fit to the data observed with the evaporation pans and tanks in Suweon area. High degree of positive correlation between Penman's predicted data and observed data with a large evaporation pan was confirmed. and the regression enquation was Y=0.7436X+17.2918, where Y represents evaporation rate from large evaporation pan, in mm/10days, and X represents potential evapotranspiration rate estimated by use of Penman's formula. 3. Evapotranspiration, Et, could be estimated from the potential evapotranspiration, Etp, by introducing the consumptive use coefficient, Kc, which was repre sensed by the following relationship: Kc=Kco$.$Ka＋Ks‥‥‥(Eq. 6) where Kco : crop coefficient Ka : coefficient depending on the soil moisture content Ks : correction coefficient a. Crop coefficient. Kco. Crop coefficients of barley, bean, and wheat for each growth stage were found to be dependent on the crop. b. Coefficient depending on the soil moisture content, Ka. The values of Ka for clay loam, sandy loam, and loamy sand revealed a similar tendency to those of Pierce type. c. Correction coefficent, Ks. Following relationships were established to estimate Ks values: Ks=Kc-Kco$.$Ka, where Ks=0 if Kc,=Kco$.$K0$\geq$1.0, otherwise Ks=1-Kco$.$Ka 4. Effective rainfall, Re, was estimated by using following relationships : Re=D, if R-D$\geq$0, otherwise, Re=R 5. The difference between rainfall, R, and the soil moisture depletion D, was taken as drainage amount, Wd. {{{{D= SUM from { {i }=1} to n (Et-Re-I+Wd)}}}} if Wd=0, otherwise, {{{{D= SUM from { {i }=tf} to n (Et-Re-I+Wd)}}}} where tf=2∼3 days. 6. The curves and their corresponding empirical equations for the variation of soil moisture depending on the soil types, soil depths are shown on Fig. 8 (a,b.c,d). The general mathematical model on soil moisture variation depending on seasons, weather, and soil types were as follow: {{{{SMC= SUM ( { C}_{i }Exp( { - lambda }_{i } { t}_{i } )+ { Re}_{i } - { Excess}_{i } )}}}} where SMC : soil moisture content C : constant depending on an initial soil moisture content $\lambda$ : constant depending on season t : time Re : effective rainfall Excess : drainage and excess soil moisture other than drainage. The values of $\lambda$ are shown on Table 1. 7. The timing and amount of irrigation could be predicted by the equation (9-a) and (9-b,c), respectively. 8. Under the given conditions, the model for scheduling irrigation was completed. Fig. 9 show computer flow charts of the model. a. To estimate a potential evapotranspiration, Penman's equation was used if a complete observed meteorological data were available, and Jensen-Haise's equation was used if a forecasted meteorological data were available, However none of the observed or forecasted data were available, the equation (15) was used. b. As an input time data, a crop carlender was used, which was made based on the time when the growth stage of the crop shows it's maximum effective leaf coverage. 9. For the purpose of validation of the models, observed data of soil moiture content under various conditions from May, 1975 to July, 1975 were compared to the data predicted by Model-I and Model-II. Model-I shows the relative error of 4.6 to 14.3 percent which is an acceptable range of error in view of engineering purpose. Model-II shows 3 to 16.7 percent of relative error which is a little larger than the one from the Model-I. 10. Comparing two models, the followings are concluded: Model-I established on the theoretical background can predict with a satisfiable reliability far practical use provided that forecasted meteorological data are available. On the other hand, Model-II was superior to Model-I in it's simplicity, but it needs long period and wide scope of observed data to predict acceptable soil moisture content. Further studies are needed on the Model-II to make it acceptable in practical use.

• The Korean Journal of Applied Statistics
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• v.14 no.1
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• pp.39-57
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• 2001

Categorical data has sometimes misclassification errors. If this data will be analyzed, then estimated cell probabilities could be biased and the standard Pearson X2 tests may have inflated true type I error rates. On the other hand, if we regard wellclassified data with misclassified one, then we might spend lots of cost and time on adjustment of misclassification. It is a necessary and important step to ask whether categorical data is misclassified before analyzing data. In this paper, when data is misclassified at one of two variables for two-dimensional contingency table and marginal sums of a well-classified variable are fixed. We explore to partition marginal sums into each cells via the concepts of Bound and Collapse of Sebastiani and Ramoni (1997). The double sampling scheme (Tenenbein 1970) is used to obtain informations of misclassification. We propose test statistics in order to solve misclassification problems and examine behaviors of the statistics by simulation studies.

• Journal of Intelligence and Information Systems
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• v.17 no.4
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• pp.157-173
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• 2011

As the Internet use explodes recently, the malicious attacks and hacking for a system connected to network occur frequently. This means the fatal damage can be caused by these intrusions in the government agency, public office, and company operating various systems. For such reasons, there are growing interests and demand about the intrusion detection systems (IDS)-the security systems for detecting, identifying and responding to unauthorized or abnormal activities appropriately. The intrusion detection models that have been applied in conventional IDS are generally designed by modeling the experts' implicit knowledge on the network intrusions or the hackers' abnormal behaviors. These kinds of intrusion detection models perform well under the normal situations. However, they show poor performance when they meet a new or unknown pattern of the network attacks. For this reason, several recent studies try to adopt various artificial intelligence techniques, which can proactively respond to the unknown threats. Especially, artificial neural networks (ANNs) have popularly been applied in the prior studies because of its superior prediction accuracy. However, ANNs have some intrinsic limitations such as the risk of overfitting, the requirement of the large sample size, and the lack of understanding the prediction process (i.e. black box theory). As a result, the most recent studies on IDS have started to adopt support vector machine (SVM), the classification technique that is more stable and powerful compared to ANNs. SVM is known as a relatively high predictive power and generalization capability. Under this background, this study proposes a novel intelligent intrusion detection model that uses SVM as the classification model in order to improve the predictive ability of IDS. Also, our model is designed to consider the asymmetric error cost by optimizing the classification threshold. Generally, there are two common forms of errors in intrusion detection. The first error type is the False-Positive Error (FPE). In the case of FPE, the wrong judgment on it may result in the unnecessary fixation. The second error type is the False-Negative Error (FNE) that mainly misjudges the malware of the program as normal. Compared to FPE, FNE is more fatal. Thus, when considering total cost of misclassification in IDS, it is more reasonable to assign heavier weights on FNE rather than FPE. Therefore, we designed our proposed intrusion detection model to optimize the classification threshold in order to minimize the total misclassification cost. In this case, conventional SVM cannot be applied because it is designed to generate discrete output (i.e. a class). To resolve this problem, we used the revised SVM technique proposed by Platt(2000), which is able to generate the probability estimate. To validate the practical applicability of our model, we applied it to the real-world dataset for network intrusion detection. The experimental dataset was collected from the IDS sensor of an official institution in Korea from January to June 2010. We collected 15,000 log data in total, and selected 1,000 samples from them by using random sampling method. In addition, the SVM model was compared with the logistic regression (LOGIT), decision trees (DT), and ANN to confirm the superiority of the proposed model. LOGIT and DT was experimented using PASW Statistics v18.0, and ANN was experimented using Neuroshell 4.0. For SVM, LIBSVM v2.90-a freeware for training SVM classifier-was used. Empirical results showed that our proposed model based on SVM outperformed all the other comparative models in detecting network intrusions from the accuracy perspective. They also showed that our model reduced the total misclassification cost compared to the ANN-based intrusion detection model. As a result, it is expected that the intrusion detection model proposed in this paper would not only enhance the performance of IDS, but also lead to better management of FNE.

• Journal of the Korean Society for Nondestructive Testing
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• v.29 no.1
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• pp.1-9
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• 2009

This paper presents stress distribution around a central crack tip in a tensile plate using phase-shifting photoelasticity and a power series stress function. Isochromatic data along the straight lines far from the crack tip were obtained by phase shifting photoelasticity and were used as input data of the hybrid experimental analysis. By using the complex-type power series stress equations, the photoelastic stress distribution fields in the vicinity of the crack and the mode I stress intensity factor were obtained. With the help of image processing software, accuracy and reliability was enhanced by twice multiplying and sharpening the measured isochromatics. Actual and reconstructed fringes were compared qualitatively. For quantitative comparison, percentage errors and standard deviations of the percentage errors were calculated for all measured input data by varying the number of terms in the stress function. The experimental results agreed with those predicted by finite element analysis and empirical equation within 2 percent error.

• Transactions of Materials Processing
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• v.26 no.5
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• pp.271-276
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• 2017

A tee is the most common pipefitting used to combine or divide fluid flow. Tees can connect pipes of different diameters or change the direction of a pipe run. To manufacture tee type of stainless steel pipe, combinations of punch piercing and burr forming have been widely used in the industry. However, such method is considerably time consuming with regard to performing empirical work necessary to attain process conditions to prevent upper end tearing of the tee product and meet target tee height. Numerous experiments have shown that the piercing profile is the main cause of defects mentioned above. Furthermore, the mold design is formed through trial and error according to pipe diameters and changes in requirements. Thus, the objective of this study was to perform piercing and burring process analysis via finite element analysis using DYNAFORM to resolve problems mentioned above. An optimization design method was used to determine the piercing punch profile. Three radii of the piercing punch (i.e., large, small, and joined radii) were selected as design variables to minimize thinning of a tee pipe. Based on results of correlation and multiple regression analyses, we developed a predictive approximation model to satisfy requirements for both thickness reduction and target height. The new piercing punch profile was then applied to actual tee forming using the developed prediction equation. Model results were found to be in good agreement with experimental results.