• 통합자연과학논문집
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• 제12권3호
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• pp.91-99
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• 2019

Many researchers in various study fields use the two sample t-test to confirm their treatment effects. The two sample t-test is generally used for small samples, and assumes that two independent random samples are selected from normal populations, and the population variances are unknown. Researchers often conduct F-test, the test of equality of variances, before testing the treatment effects, and the test statistic or confidence interval for the two sample t-test has two formats according to whether the variances are equal or not. Researchers using the two sample t-test often want to know how large sample sizes they need to get reliable test results. This research gives some guidelines for sample sizes to them through simulation works. The simulation had run for normal populations with the different ratios of two variances for different sample sizes (${\leq}30$). The simulation results are as follows. First, if one has no idea equality of variances but he/she can assume the difference is moderate, it is safe to use sample size at least 20 in terms of the nominal level of significance. Second, the power of F-test for the equality of variances is very low when the sample sizes are small (<30) even though the ratio of two variances is equal to 2. Third, the sample sizes at least 10 for the two sample t-test are recommendable in terms of the nominal level of significance and the error limit.

• 통합자연과학논문집
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• 제14권3호
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• pp.123-129
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• 2021

This research examines the effect of positively skewed population distribution on the two sample t-test through simulation. For simulation work, two independent samples were selected from the same chi-square distributions with 3, 5, 10, 15, 20, 30 degrees of freedom and sample sizes 3, 5, 10, 15, 20, 30, respectively. Chi-square distribution is largely skewed to the right at small degrees of freedom and getting symmetric as the degrees of freedom increase. Simulation results show that the sampled populations are distributed positively skewed like chi-square distribution with small degrees of freedom, the F-test for the equality of variances shows poor performances even at the relatively large degrees of freedom and sample sizes like 30 for both, and so it is recommended to avoid using F-test. When two population variances are equal, the skewness of population distribution does not affect on the t-test in terms of the confidence level. However even though for the highly positively skewed distribution and small sample sizes like three or five the t-test achieved the nominal confidence level, the error limits are very large at small sample size. Therefore, if the sampled population is expected to be highly skewed to the right, it will be recommended to use relatively large sample size, at least 20.

• 통합자연과학논문집
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• 제15권1호
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• pp.9-18
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• 2022

This research examines the power of bootstrap two-sample test, and compares it with the powers of two-sample t-test and Wilcoxon rank sum test, through simulation. For simulation work, a positively skewed and heavy tailed distribution was selected as a population distribution, the chi-square distributions with three degrees of freedom, χ²₃. For two independent samples, the fist sample was selected from χ²₃. The second sample was selected independently from the same χ²₃ as the first sample, and calculated d+ax for each sampled value x, a randomly selected value from χ²₃. The d in d+ax has from 0 to 5 by 0.5 interval, and the a has from 1.0 to 1.5 by 0.1 interval. The powers of three methods were evaluated for the sample sizes 10,20,30,40,50. The null hypothesis was the two population medians being equal for Bootstrap two-sample test and Wilcoxon rank sum test, and the two population means being equal for the two-sample t-test. The powers were obtained using r program language; wilcox.test() in r base package for Wilcoxon rank sum test, t.test() in r base package for the two-sample t-test, boot.two.bca() in r wBoot pacakge for the bootstrap two-sample test. Simulation results show that the power of Wilcoxon rank sum test is the best for all 330 (n,a,d) combinations and the power of two-sample t-test comes next, and the power of bootstrap two-sample comes last. As the results, it can be recommended to use the classic inference methods if there are widely accepted and used methods, in terms of time, costs, sometimes power.

• Journal of the Korean Data and Information Science Society
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• 제21권6호
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• pp.1243-1251
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• 2010

임상시험을 시행하는 경우 위약을 신약과 비교하는 경우가 대다수이다. 기존에 독립인 두 모 집단의 표본수를 계산하는 방법으로 모수적 방법에서는 t검정을 이용하였고, 비모수적 방법에서는 Wilcoxon 순위합검정 (Wilcoxon, 1945)을 이용하였다. 본 논문에서는 Orban과 Wolfe (1982)가 제안한 선형위치통계량의 검정법과, Kim (1994)이 선형위치통계량에 기초하여 계산한 검정력의 결과를 이용하여 표본수 구하는 방법을 제안한다. 또한 앞서 제안한 방법의 표본수를 기존의 Wilcoxon 순위합검정을 이용하여 Wang 등 (2003)이 제안한 공식을 이용한 표본수, 그리고 모수적 방법을 이용한 t검정의 표본수와 비교하였다.

• 대한치과의사협회지
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• 제52권9호
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• pp.558-569
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• 2014

Sample size determination is critical, but not easy to do. Sample size defined as the number of observations in a sample to be studied should be big enough to have a high likelihood of detecting a true difference between groups. Practical procedure for determining sample size, using $G^*$power and previous dental articles, was shown in this study. Examples involving independent t-test, paired t-test, one-way analysis of variance(ANOVA), and one-way repeated-measures(RM) ANOVA were used. The purpose of this study is to enable researchers with non-statistical backgrounds to use in practice freely available statistical software G*power to determine sample size and power.

• 한국간호교육학회지
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• 제15권1호
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• pp.120-127
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• 2009

Purpose: In the literature power analysis in experimental studies is often executed and reported falsely. This descriptive study was done to promote the correct application of the Cohen(1988)'s power analysis method. Method: Articles of experimental studies from a nursing journal were selected and reviewed to examine the uses of and the reports on the power analysis process. Also, the appropriate power analysis process was discussed with an example of the most common experimental design, an independent two-group design with t test analysis plan. Result: Around half the experimental studies examined reported that they carried out power analysis. Cohen's method was the most frequently utilized but with accuracy in question. Conclusion: Power analysis to estimate sample size is the interplay between alpha, power, and effect size, and other factors in the case of t test analysis. Researchers should have a clear understanding of how to apply the Cohen's power analysis method so they do not produce poorly estimated sample sizes.

• 대한한의진단학회지
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• 제12권1호
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• pp.22-41
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• 2008

Background: Eight-Constitution Medicine (ECM) devides the human body into eight constitutions. Up until now, checking the pulse types is only way to classify the eight constitution. Recently we try to make a questionnaire that is based on the Eight-Constitution characters and analyze the answer from patients who were classified into one of the eight constitutions according to their pulse types and their responses to constitution-acupuncture therapy Objective: This study intends to analyze each answer of the Eight-Constitution Questionnaire with independent sample t-test. Methods: Participants of this study were outpatients in ECM clinics located in Korea. The resources were collected from 925 patients who were classified into one of the eight constitutions according to their pulse types and their responses to constitution-acupuncture therapy. SPSS 13.0 for Windows was used for independent sample t-test. Results and Conclusions: 1. The proportion of participants' constitutions is in the order of Pancreotonia (28.0%), Colonotonia (17.3%), Pulmotonia (18.1%), Hepatonia (18.1%), Vesicotonia (8.5%), Cholecystotonia (7.0%), Renotonia (2.6%) and Gastrotonia (0.4%). 2. Eight-Constitution Questionnaire consists of 5 parts; Appearance, Character, Body reaction, Physiology & Pathology and Food reaction. 3. 10 items were chosen among 42 question about Appearance. 4. Due to the deficiency of Gastrotonia examples, useful items have to be given up. If we can gather Gastrotonia examples, we can use meaningful items more than 10.

• 대한한의진단학회지
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• 제13권1호
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• pp.89-110
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• 2009

Background : Eight-Constitution Medicine (ECM) devides the human body into eight constitutions. Up until now, checking the pulse types is only way to classify the eight constitution. Recently we try to make a questionnaire that is based on the Eight-Constitution characters and analyze the answer from patients who were classified into one of the eight constitutions according to their pulse types and their responses to constitution-acupuncture therapy. Objective : This study intends to analyze each answer of the Eight-Constitution Questionnaire with independent sample t-test. Methods : Participants of this study were outpatients in ECM clinics located in Korea. The resources were collected from 925 patients who were classified into one of the eight constitutions according to their pulse types and their responses to constitution-acupuncture therapy. SPSS 13.0 for Windows was used for independent sample t-test. Results and Conclusions : 1. The proportion of participants' constitutions is in the order of Pancreotonia (28.0%), Colonotonia (17.3%), Pulmotonia (18.1%), Hepatonia (18.1%), Vesicotonia (8.5%), Cholecystotonia (7.0%), Renotonia (2.6%) and Gastrotonia (0.4%). 2. Eight-Constitution Questionnaire consists of 5 parts; Appearance, Character, Body reaction, Physiology & Pathology and Food reaction. 3. 18 items were chosen among 81 question about Character. 4. Due to the deficiency of Gastrotonia examples, useful items have to be given up. If we can gather Gastrotonia examples, we can use meaningful items more than 18.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• 수산해양교육연구
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• 제22권1호
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• pp.99-112
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• 2010

This study was conducted to test the effect of Burns' cognitive-behavioral group counseling on depression and anxiety of industrial high school students. For this purpose, an experimental group and comparative group which was composed of 15 students respectively were assigned. The independent sample t-test between experimental group and comparative group about the degree of pre-test and after-test and the opposition sample t-test within each experimental group and comparative group were conducted. Analysis of Covariance was also applied. Results of the analyses showed that Burns' cognitive-behavioral group counseling program was effective in decreasing depression and anxiety. Implications of these results on student guidance and counseling were discussed. Suggestions for future research were presented and limitations were indicated.