• Journal of Veterinary Clinics
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• v.28 no.4
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• pp.422-426
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• 2011

For a national survey in which wide geographic region or an entire country is targeted, multi-stage sampling approach is widely used to overcome the problem of simple random sampling, to consider both herd- and animallevel factors associated with disease occurrence, and to adjust clustering effect of disease in the population in the calculation of sample size. The aim of this study was to establish sample size for estimating bovine tuberculosis (TB) in Korea using stratified two-stage sampling design. The sample size was determined by taking into account the possible clustering of TB-infected animals on individual herds to increase the reliability of survey results. In this study, the country was stratified into nine provinces (administrative unit) and herd, the primary sampling unit, was considered as a cluster. For all analyses, design effect of 2, between-cluster prevalence of 50% to yield maximum sample size, and mean herd size of 65 were assumed due to lack of information available. Using a two-stage sampling scheme, the number of cattle sampled per herd was 65 cattle, regardless of confidence level, prevalence, and mean herd size examined. Number of clusters to be sampled at a 95% level of confidence was estimated to be 296, 74, 33, 19, 12, and 9 for desired precision of 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06, respectively. Therefore, the total sample size with a 95% confidence level was 172,872, 43,218, 19,224, 10,818, 6,930, and 4,806 for desired precision ranging from 0.01 to 0.06. The sample size was increased with desired precision and design effect. In a situation where the number of cattle sampled per herd is fixed ranging from 5 to 40 with a 5-head interval, total sample size with a 95% confidence level was estimated to be 6,480, 10,080, 13,770, 17,280, 20.925, 24,570, 28,350, and 31,680, respectively. The percent increase in total sample size resulting from the use of intra-cluster correlation coefficient of 0.3 was 22.2, 32.1, 36.3, 39.6, 41.9, 42.9, 42,2, and 44.3%, respectively in comparison to the use of coefficient of 0.2.

• The Journal of the Korea Contents Association
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• v.18 no.2
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• pp.468-475
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• 2018

The current system of making course evaluations mandatory in universities in Korea in order to supplement low participation levels is a major hindering factor for the validity of the evaluation results due to students' insincere responses. This study points out the problems in course evaluations that are in the form of surveys and instead proposes a sample course evaluation system that utilizes a sample mean to deduce a population mean, attempting to prove through simulation that this is statistically significant. Thus, small, medium, and large scale courses as well as cyber courses that were available in S University in the fall 2016 semester were set as the population, and each course's evaluation average grade was set as the population mean. Furthermore, we used the average grade and standard deviation of the same courses from the previous year in order to decide the sample number, the reliability level was set as 95%, and the margin of error was set as ${\pm}0.25$. As a result of carrying out a simulation using the data analysis tool R, all the courses (small scale, medium scale, large scale, and cyber) showed to have a reliability level close to 95% including the population mean, and consequently practicality of the representative sample course evaluation system was proven.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1211-1219
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• 2013

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.

• Journal of Korean Society for Quality Management
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• v.33 no.3
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1449-1454
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• 2009

The performance variation of a multibody system is affected by a variation of various design variables of the system. And the effects of design variable variations on the performance variation must be considered in design of a multibody system. Accordingly, a variation analysis of a multibody system needs to be conducted in design of a multibody system. For a variation analysis of a performance, population mean and variance which are called statistical parameters of design variables are needed. However, an evaluation of statistical parameters of design variables is impossible in many practical cases. Therefore, an estimation of statistical parameters of the performance based on sample mean and variance which are called statistic of design variables is needed. In this paper, the variation analysis method for a multibody system based on design variable samples was proposed. And, using the proposed method, a variation analysis of the vehicle ride comfort based on sample statistic of design variables was conducted.

• Journal of Korean Society for Quality Management
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• v.22 no.2
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• pp.89-97
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• 1994

We consider the linear calibration model: $y_1={\alpha}+{\beta}x_i+{\sigma}{\varepsilon}_i$, i = 1, ${\cdots}$, n, $y={\alpha}+{\beta}x+{\sigma}{\varepsilon}$ where ($y_1$, ${\cdots}$, $y_n$, y) stands for an observation vector, {$x_i$} fixed design vector, (${\alpha}$, ${\beta}$) vector of regression parameters, x unknown true value of interest and {${\varepsilon}_i$}, ${\varepsilon}$ are mutually uncorrelated measurement errors with zero mean and unit variance but otherwise unknown distributions. On the basis of simple small-sample low-noise approximation, we introduce a new method of comparing the mean squared errors of the various competing estimators of the true value x for finite sample size n. Then we show that a class of estimators including the classical and the inverse estimators are consistent and first-order efficient within the class of all regular consistent estimators irrespective of type of measurement errors.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Journal of Nutrition and Health
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• v.17 no.2
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• pp.137-144
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• 1984

Due to the fact that blood gathering is not readily accepted by people, it has been difficult to make a full-scale study on zinc through blood analysis. For that reason, in this paper, a correlation of zinc contents in serum and hair was studied to find out whether only hair, which is relatively easy to collect, can be used for a measurement of zinc content. The subjects were 47 healthy female collegians selected at random whose average age was 22, mean height 159.1cm and average weight 49.7kg. The mean zinc value in serum of subjects was ${107.1}\pm{29.0}{\mu}g{/100ml}$, while the mean value in hair was ${150.2}\pm{42.7}ppm$. Correlation analysis shows that there was a significant correlation in zinc contents of serum and hair ( p<0.01). The results shows that measuring zinc level by using only hair samples would be satisfactory. But the use of hair sample for a measurement of zinc level has one demerit. That is, the method is more likely to be subjected to contamination because it makes more complicated procedures in sample preparation than the method of using blood sample.

• Korean Journal of Environmental Biology
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• v.32 no.3
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• pp.211-215
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• 2014

In order to accurately estimate the litter mass, we evaluated the required sample sizes across 13 chronosequence stands for five years (1994~1996, 2003~2004) in northern hardwood forests in New Hampshire, USA. It was found that the number of required litter traps in our stands (0.25~0.5 ha) within ${\pm}10%$ of the sample mean was appeared to be similar or higher than the 15 litter traps installed in this study. Notably, in 1994 and 1995, the number of required litter trap was twice higher than the 15 litter traps. Further, within ${\pm}20%$ of the sample mean, the number of required litter traps was less than 10 across all 13 stands for five years, which indicates that we can reduce the sample size. Precisely, the number of sample size had increased in stands with steep and high elevation, but no relations with stand age across 13 stands were observed. Based on these results, we suggest that it is important to sample litter mass for several years, in order to determine the number of appropriate sample size, and stands with steep and high elevation may need more litter traps.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.105-117
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• 2004

In this paper, a new method is developed for estimating the mean of a population which has a linear trend. This method involves drawing a sample by the modified systematic sampling, and then estimating the population mean with an adjusted estimator, not with the sample mean itself. We use the method of least squares in determining the adjusted estimator. The proposed method is shown to be more and more efficient as the linear trend becomes stronger. It turns out to be relatively efficient as compared with the conventional methods if $\sigma$$^2$the variance of the random error term in the infinite superpopulation model, is not very large.