• 제목/요약/키워드: two-sample test

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Effective Sample Sizes for the Test of Mean Differences Based on Homogeneity Test

  • Heo, Sunyeong
    • 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.

Comparison of the Power of Bootstrap Two-Sample Test and Wilcoxon Rank Sum Test for Positively Skewed Population

  • Heo, Sunyeong
    • 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.

Effect of Positively Skewed Distribution on the Two sample t-test: Based on Chi-square Distribution

  • Heo, Sunyeong
    • 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.

두 모집단 모평균 비교의 지도에 관한 연구 (A Study on Teaching Method of Two-Sample Test for Population Mean Difference)

  • 김용태;이장택
    • 한국수학교육학회지시리즈A:수학교육
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    • 제45권2호
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    • pp.145-154
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    • 2006
  • The main purpose of this study is to investigate the effect of departures from normality and equal variance on the two-sample test when the variances are unknown. We have found that type I error brought about a little bit change which is ignorable in relation to kurtosis. But the change of type I error was mainly based on the skewness of the parent population. In introductory statistics classes where data analysis includes techniques for detecting skewness of two populations, we recommend the two-sample t-test when maximal skewness of two populations is smalter than the value 4 when the variances seem equal. Furthermore, our simulations reveal that the two-sample t-test appears somewhat more robust than that of z-test if the assumption of equal variance is satisfied. In the case of unequal variance, the two-sample t-test appears somewhat more robust provided the t-statistic using Satterthwaite's approximate degrees of freedom.

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TWO-SAMPLE COMPARISON USING SIGN TEST ON RANKED-SET SAMPLES

  • Kim, Dong-Hee;Kim, Young-Cheol
    • Journal of applied mathematics & informatics
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    • 제5권1호
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    • pp.263-268
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    • 1998
  • This paper proposes the two-sample comparison us-ing sign test based on ranked-set sample(RSS). We investigate the asymptotic properties of the proposed test statistic and compare the asymptotic relative efficiencies of the proposed test statistic with re-spect to Mann-Whitney-Wilcoxon test statistic based on RSS and Mann-Whitney-Wilcoxon test statistic based on the simple random sample(SRS).

Bootstrap Tests for the General Two-Sample Problem

  • 조길호;정성화
    • Journal of the Korean Data and Information Science Society
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    • 제13권1호
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    • pp.129-137
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    • 2002
  • Two-sample problem is frequently discussed problem in statistics. In this paper we consider the hypothese methods for the general two-sample problem and suggest the bootstrap methods. And we show that the modified Kolmogorov-Smirnov test is more efficient than the Kolmogorov-Smirnov test.

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약의존성 잡음에서 두 표본을 쓰는 국소 최적 확률 신호 검파기의 검정 통계량 (The Test Statistic of the Two Sample Locally Optimum Rank Detector for Random Signals in Weakly Dependent Noise Models)

  • 배진수
    • 한국통신학회논문지
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    • 제35권8C호
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    • pp.709-712
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    • 2010
  • 이 논문에서는 시간상 확률 상관이 0이 아닌 약의존성 잡음 모형에서 두 표본을 쓰는 국소 최적 순위 검파기의 검정 통계량를 얻었다. 기준 관측과 보통 관측으로 이루어진 두 표본 관측 모형에서 약의존성 잡음 환경에 알맞은 국소 최적 순위 검파기의 검정 통계량을 네이먼 피어슨 정리로부터 유도하였다. 두 표본을 쓰는 국소 최적 순위 검파기는 한 표본을 쓰는 국소 최적 순위 검파기와 같은 점근 성능을 가지며 부호 통계량을 다룰 필요가 없어 얼개가 비교적 간단하다.

잡음영상에서 효과적인 에지검출을 위한 이표본 선형 순위 검정법 (Two-sample Linear Rank Tests for Efficient Edge Detection in Noisy Images)

  • 임동훈
    • 한국컴퓨터정보학회논문지
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    • 제11권4호
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    • pp.9-15
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    • 2006
  • 본 논문에서는 잡음영상에서 효과적인 에지검출을 위해 이표본 위치문제(two-sample location Problem)에서 잘 알려진 선형 순위 검정법(linear raft test)인 Wilcoxon 검정법, Median 검정법 그리고 Van der Waerden 검정법을 적용하고자 한다. 에지 존재 유무는 에지-높이 모수(edge-height parameter)를 사용한 모형 하에서 인접한 두 개의 근방영역간의 평균 차이를 검정함으로서 통계적으로 결정한다. 여기서 근방영역의 크기와 형태는 에지검출을 위한 계산 속도와 에지방향을 고려하여 적응성 있게(adaptively) 결정하였다. 통계적 방법들의 에지검출 성능을 평가하기 위해 자연영상(natural images)과 인조영상(synthetic images) 그리고 잡음이 추가된 영상에 대해 실험을 실시하고 비교 분석하였다.

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Asymptotic Relative Efficiency of t-test Following Transformations

  • Yeo, In-Kwon
    • Journal of the Korean Statistical Society
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    • 제26권4호
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    • pp.467-476
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    • 1997
  • The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

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Depth-Based rank test for multivariate two-sample scale problem

  • Digambar Tukaram Shirke;Swapnil Dattatray Khorate
    • Communications for Statistical Applications and Methods
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    • 제30권3호
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    • pp.227-244
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    • 2023
  • In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.