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

• Communications for Statistical Applications and Methods
• /
• 제17권1호
• /
• pp.79-88
• /
• 2010

기초통계학의 수업에서 두 집단간 평균의 차이를 검정함에 있어 두 집단의 분산의 동질성 여부에 따라 다른 통계 절차를 사용할 것을 제안하고 있다. 이러한 이유로 통계 분석에 사용되는 SAS나 SPSS 등의 패키지에서는 두 집단의 평균 차이의 검정에 앞서 분산의 동질성 검정을 선행할 것을 제안한다. 하지만, 이전의 몇몇 연구에서 알려진 바와 같이 이러한 이 단계 검정 절차는 검정의 유의수준(제 1종의 오류)을 제어하기가 어렵다. 본 글에서는 이 단계 검정을 행함에 있어 1 단계와 2 단계의 유의수준 ${\alpha}_1$과 ${\alpha}_2$를 조절하여 전체 검정의 유의수준을 주어진 ${\alpha}$ 이하로 제어하는 절차를 소개한다.

• Journal of the Korean Data and Information Science Society
• /
• 제16권3호
• /
• pp.609-620
• /
• 2005

In the secondary data analysis for categorical data, situations often arise in which the estimated cell variances are available, but not the full matrix of variances. In this case researchers are often inclined to use Pearson-type test statistics for homogeneity. However, for a complex sample observed cell proportions are not distributed as multinomial and Pearson-type test statistic generally is not distributed asymptotically as chi-square distribution. This paper evaluates powers for Wald test and Pearson-type test and the first order corrected test of Pearson-type test for homogeneity. The resulting power curves indicate that as the misspecification effect increases, the amount of inflation of significance level and the loss of power Pearson-type test are getting more severe.

• Communications for Statistical Applications and Methods
• /
• 제9권3호
• /
• pp.853-864
• /
• 2002

In the analysis of categorical data subject to misclassification errors, the observed cell proportions are adjusted by a misclassification probabilities and estimates of variances are adjusted accordingly. In this case, it is important to determine the extent to which misclassification probabilities are homogeneous within a population. This paper considers methods to evaluate the power of chi-squared tests for homogeneity with complex survey data subject to misclassification errors. Two cases are considered: adjustment with homogeneous misclassification probabilities; adjustment with heterogeneous misclassification probabilities. To estimate misclassification probabilities, logistic regression method is considered.

• Communications for Statistical Applications and Methods
• /
• 제16권2호
• /
• pp.389-396
• /
• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• 통합자연과학논문집
• /
• 제7권3호
• /
• pp.208-213
• /
• 2014

National-wide and/or large scale sample surveys generally use complex sample design. Traditional Pearson chi-square test is not appropriate for the categorical complex sample data. Rao-Scott suggested an adjustment method for Pearson chi-square test, which uses the average of eigenvalues of design matrix of cell probabilities. This study is to compare the efficiency of Rao-Scott first order adjusted test to Wald test for homogeneity between two populations using 2009 Gyeongnam regional education offices's customer satisfaction survey (2009 GREOCSS) data. The 2009 GREOCSS data were collected based on stratified three-stage cluster sampling with probability proportional to size. The empirical results show that the Rao-Scott adjusted test statistic using only the variances of cell probabilities is very close to the Wald test statistic, which uses the covariance matrix of cell probabilities, under the 2009 GREOCSS data based. However it is necessary to be cautious to use the Rao-Scott first order adjusted test statistic in the place of Wald test because its efficiency is decreasing as the relative variance of eigenvalues of the design matrix of cell probabilities is increasing, specially more when the number of degrees of freedom is small.

• Journal of the Korean Data and Information Science Society
• /
• 제16권2호
• /
• pp.195-205
• /
• 2005

In decision tree analysis, C4.5 and CART algorithm have some problems of computational complexity and bias on variable selection. But QUEST algorithm solves these problems by dividing the step of variable selection and split point selection. When input variables are continuous, QUEST algorithm uses ANOVA F-test under the assumption of normality and homogeneity of variances. In this paper, we investigate the influence of violation of normality assumption and effect of the transformation of variables in the QUEST algorithm. In the simulation study, we obtained the empirical powers of variable selection and the empirical bias of variable selection after transformation of variables having various type of underlying distributions.

• Communications for Statistical Applications and Methods
• /
• 제31권1호
• /
• pp.1-35
• /
• 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.

• 대한의용생체공학회:의공학회지
• /
• 제19권6호
• /
• pp.551-562
• /
• 1998

SPECT 이상조직 검출능에 근거한 투사 영상의 다해상도 필터링 기법이 SPECT 영상 재구성 문제에 대한 한 최적 해를 제공할 수 있다. 본 논문에서는, 이전 연구 결과와 관련하여, 주어진 물리적 조건하에서의 SPECT 이상조직 검출능을 m개의 최소 검출가능 이상조직 크기 (MDLS)로 예측하고, 각 MDLS에 의존하는 해상도 $\frac{MDLS}{4\sqrt{2In2}}$를 유지하는 수준에서 잡음 억제 효과를 최대화하도록 설계된 m개의 재구성 필터를 구성시켰다. 제안된 다해상도 필터링 기법은, 주어진 투사 영상으로부터 이들 필터들을 적용하여 얻어진 m개 수준 해상도의 필터 영상에 coarse-to-fine 접근방법을 사용하였다. 먼저 필터 영상 각각에 대하여, 각 화소를 중심으로 한 창에서 계산된 지역 분산값과 지역 분산 분포로부터 결정된 최빈값을 비교함으로써 지역 균일도를 결정한다. 지역 균일도에 근거하여, 해상도가 가장 낮은 필터 영상으부터 균일한 영역으로 추정되는 화소들을 찾아 그 화소 값을 취하고, 나머지 화소에 대해서는 점점 해상도가 높은 필터 영상으로부터 균일 영역 화소를 찾는 과정을 반복한다. 균일 영역 화소를 찾는 반복 과정을 마친 후에도 여전히 윤곽선 영역으로 암아 있는 화소들에 대해서는 최고 해상도 필터 영상의 화소 값이 대체된다. 모의 실험 수행 결과, 제안된 다해상도 필터링 기법은 투사 영상의 균일 지역에서는 강한 평활화 효과를 보이는 반면 윤곽선 지역에서는 우수한 해상도 향상 효과를 보였으며, 이에 따라 재구성 영상에서의 우수한 적응적 효과를 제공하였다.

• Journal of Acupuncture Research
• /
• 제37권2호
• /
• pp.110-117
• /
• 2020

Background: The aim of this pilot study was to assess the safety and dosing of scolopendrid pharmacopuncture (SPP). Methods: A total of 40 healthy Sprague-Dawley rats (males and 20 females 20) were selected following a 7-day inspection and acclimation period. SPP was administered via intramuscular injection, over a 2-week period using 3 doses including a high-dose [0.84 mg of scolopendrid per kg of body weight (BW)], a med-dose (0.42 mg/kg BW), and a low-dose (0.21 mg/kg BW). The control group was injected with sterile water into the muscles. Unusual changes caused by administration of the test substance were observed. Weight, feed intake, organ weight, and hematological examinations were compared among the groups. Using the SPSS statistical program, Levene's test was performed to evaluate the homogeneity of variances, and a one-way ANOVA test was subsequently performed to assess the significance between each test group. Results: During the experiment no animals died. Weight change, food consumption, organ weight, hematological test, and blood biochemical tests showed no significant differences in the treatment groups compared to controls. Conclusion: No toxicological changes related to the administration of test substances were observed. Therefore, the LD₅₀ (lethal-dose that kills 50%) of scolopendrid pharmacoupuncture in rats was greater than 0.84 mg/kg.