• Journal of the Korean School Mathematics Society
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• v.21 no.3
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• pp.247-266
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• 2018

In this paper, three main concepts are chosen for this statistical estimation study, based on previous studies: confidence interval and reliability, sampling distribution of mean and population mean estimation, and relationships between elements of confidence interval. The main objectives of this study are as follows: 1. How are the attitudes that future math teachers and high school students have to ward the statistical estimation? 2. Is there some difference in the awareness of misconceptions about the statistical estimation that future math teachers and high school students have? A study result shows that both groups have difficulties in understanding statistical concepts and their meaning used in Unit Statistical Estimation. They tend to wrongly think that the meaning of reliability is the same as that of probability. They also have difficulties in understanding sample variance in the sampling distribution of mean, which makes it impossible to connect with population mean estimation. It is shown that relationships between elements consisting of confidence interval are not consistent.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.269-277
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• 2000

We propose the Bayesian testing for the equality of two log-normal population means. Specifically we use the intrinsic Bayes factors suggested by Berger and Perichi (1996, 1998) based on the noninformative priors for the parameters. In order to investigate the usefulness of the proposed Bayesian testing procedures, we compare it with classical tests via both real data analysis and simulation.

• Science of Emotion and Sensibility
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• v.17 no.2
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• pp.63-76
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• 2014

Although most behavioral reaction times (RTs) for cognitive tasks exhibit positively skewed distributions, the majority of studies primarily rely on a measure of central tendency (e.g. mean) which can cause misinterpretations of data's underlying property. The purpose of current study is to introduce procedures for describing characteristics of RT distributions, thereby effectively examine the influence of experimental manipulations. On the basis of assumption that RT distribution can be represented as a convolution of Gaussian and exponential variables, we fitted the ex-Gaussian function under a maximum-likelihood method. The ex-Gaussian function provides quantitative parameters of distributional properties and the probability density functions. Here we exemplified distributional analysis by using empirical RT data from two conventional visual search tasks, and attempted theoretical interpretation for setsize effect leading proportional mean RT delays. We believe that distributional RT analysis with a mathematical function beyond the central tendency estimates could provide insights into various theoretical and individual difference studies.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.153-161
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• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.633-644
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• 1998

혼합설계의 교호작용에 대한 F 검정이 유효하려면 다표본 구형성(multisample sphericity) 가정과 다변량 정규분포 가정이 만족되어야 한다. F 검정을 실시하기 위한 가정들이 위반된 조건하에서 혼합설계의 교호작용에 대한 검정법들의 1종오류가 비교되었다. 비교된 검정법들은 (1) F 검정(F), (2) 절사평균을 사용한 F 검정($F_T$)(3)$\varepsilon$-수정 F 검정($\varepsilon)$(4) 절사평균을 사용한 $\varepsilon$-수정 F 검정$(\varepsilon_T$) (5) CIGA검정(CIGA), (6) 절사평균을 사용한 CIGA검정($CIGA_T$)이었다. 결과는 CIGA와 $CIGA_T$는 1종오류를 대체로 잘 관리하나, F검정들과 ($\varepsilon$)검정들은 일부 조건에서 아주 작은 1종오류나 아주 큰 1종오류를 갖는 것으로 나타났다.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.89-100
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• 1994

In this paper we consider a new estimator of mean residual life (MRL), based on the partial moment of the distribution. The parameters of a partial moment are estimated by its maximum likelihood estimators when the underlying distribution is known. Though the new estimator is not a consistent estimator of the MRL, it is shown to have smaller mean squared error than the well known empirical MRL estimator for certain parametric families. Numerical summaries of the mean squared errors of the new estimator are presented.

• Journal of the Korean School Mathematics Society
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• v.23 no.3
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• pp.239-257
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• 2020

This study analyzes the degree of freedom with three aspects: as academic knowledge, in the curriculum focused on textbooks, and students' understanding of the degree of freedom. The results provide five critical points. First, we need discussions on whether to include the degree of freedom in the curriculum. Second, we need to reconsider the current way textbooks are described. Third, there should be a didactical analysis to advance students' understanding of the concept of the degree of freedom. Fourth, there are limitations in learning the concept of the degree of freedom in the current textbook learning environment. Fifth, a didactical check of sampling distribution such as sample mean, sample variance, and sample standard deviation is required. The implications were drawn that the emphasis on statistical reasoning education in the curriculum and careful consideration of introducing the t-distribution curriculum was required.

• Survey Research
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• v.10 no.3
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• pp.157-172
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• 2009

For a survey research in which the characteristics of the population of interest are investigated from a sample, representativeness of the sampling frame is one of the most important part to be considered. If the sampling frame fails to represent the population properly, statistical procedures based on the even efficient sampling design result in significant nonsampling biases and thus the statistical validities of the results could be damaged. But the construction of the reliable sampling frame that covers the population properly costs money and time and thus the sampling frame based on a census or a large scale survey is often used in practice. For example, the sampling frame based on the population households census is used for many household surveys in Korea. But due to the time difference between the census and a survey of interest, the sampling frame constructed from the census is expected to fail to cover the population of interest. Especially, one could expect a large amount of population and household movement in a large city like Seoul. Thus in our research, we considered the construction of new sampling frame and the procedure of sample selection for 2008 Seoul survey. We analyzed the sampling frame based on 2005 population households census and found that it does not represent the population properly. Thus, we proposed a new sampling frame based on resident registration DB for 2008 Seoul survey. We also proposed the sampling weights and estimator of the population mean based on the sample selected from the newly constructed sampling frame.

• Journal of the Korean Society of Physical Medicine
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• v.7 no.1
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• pp.103-110
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• 2012

연구목적 : 본 연구는 노인의 성별이 낙상에 영향을 줄 수 있는 체중분포지수에 미치는 차이를 알아보고자 한다. 연구방법：광주광역시 소재 빛고을 노인건강타운 물리치료실을 이용하는 65세 이상 66명(남성 33명, 여성 33명) 노인을 대상으로 남성노인 평균연령은 70.97세, 여성노인 평균연령은 71.39세로 모든 대상자는 TETRAX의 체중분포지수(weight distribution index; WDI)를 이용하여 성별에 따라 그 차이를 비교 분석하였다. 측정 방법 은 안정된 발판에서 눈을 뜨고 정면을 향한 자세, 안정된 발판에서 눈을 감고 정면을 향한 자세, 불안정한 발판에서 눈을 뜨고 정면을 향한 자세, 불안정한 발판에서 눈을 감고 정면을 향한 자세, 안정된 발판에서 눈을 감고 고개를 오른쪽으로 돌린 자세, 안정된 발판에서 눈을 감고 고개를 왼쪽으로 돌린 자세, 안정된 발판에서 눈을 감고 고개를 뒤로 젖힌 자세, 안정된 발판에서 눈을 감고 고개를 숙인 자세로 측정하였고, 분석방법은 SPSS version 12.0을 이용하여 통계처리 하였고, 남녀 간의 안정성지수와 체중분포지수의 평균차이 검정은 독립표본 t-검정을 실시하였다. 통계학적 유의성을 검증하기 위해 ${\alpha}$는 유의수준 0.05로 하였다. 연구결과 : 성별에 따른 WDI비교에서 불안정한 발판과 안정된 발판에서 눈을 뜬 상태와 감은 상태에 정면을 향한 자세, 안정된 발판에서 눈을 감고 고개를 왼쪽과 오른쪽으로 돌린 자세에서 유의한 차이가 있었으나 안정된 발판에서 고개를 뒤로 젖힌 자세와 고개를 숙인자세에서는 유의한 차이는 없었다. 결론 : 본 연구의 결과를 바탕으로 성별에 따른 노인의 WDI에 영향을 미칠 수 있는 요인을 파악하여 낙상예방프로그램 기초자료로 활용 될 것으로 생각된다.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.29-35
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• 2011

In statistical process control, the primary method used to monitor the number of nonconformities is the c-chart. The conventional c-chart is based on the assumption that the occurrence of nonconformities in samples is well modeled by a Poisson distribution. When the Poisson assumption is not met, the X-chart is often used as an alternative charting scheme in practice. And CUSUM-chart is used when it is desirable to detect out of control situations very quickly because of sensitive to a small or gradual drift in the process. In this paper, I compare CUSUM-chart to X-chart for the Katz family covering equi-, under-, and over-dispersed distributions relative to the Poisson distribution.