A minimum combination t-test method for testing differences in population means based on a group of samples of size one

크기가 1인 표본들로 구성된 집단에 기반한 모평균의 차이를 검정하기 위한 최소 조합 t-검정 방법

  • Heo, Miyoung (Department of Applied statistics, Chung-Ang University) ;
  • Lim, Changwon (Department of Applied statistics, Chung-Ang University)
  • 허미영 (중앙대학교 응용통계학과) ;
  • 임창원 (중앙대학교 응용통계학과)
  • Received : 2017.02.24
  • Accepted : 2017.02.26
  • Published : 2017.04.30


It is often possible to test for differences in population means when two or more samples are extracted from each N population. However, it is not possible to test for the mean difference if one sample is extracted from each population since a sample mean does not exist. But, by dividing a group of samples extracted one by one into two groups and generating a sample mean, we can identify a heterogeneity that may exist within the group by comparing the differences of the groups' mean. Therefore, we propose a minimum combination t-test method that can test the mean difference by the number of combinations that can be divided into two groups. In this paper, we proposed a method to test differences between means to check heterogeneity in a group of extracted samples. We verified the performance of the method by simulation study and obtained the results through real data analysis.

일반적으로 각 N개의 모집단에서 2개 이상의 표본이 추출되었을 때, $H_0:{\mu}_1={\cdots}={\mu}_N$의 가설에 대하여 검정할 수 있지만 각 모집단으로부터 표본이 한 개씩 추출된다면 ${\bar{X}}$가 존재하지 않으므로 모평균의 차이 검정은 불가능하다. 하지만 하나씩 추출된 표본으로 구성된 집단을 두 집단으로 나누어 임의의 평균을 생성함으로써 평균의 차이를 비교한다면 표본들 사이에 존재할 수 있는 이질성을 파악할 수 있다. 따라서 우리는 두 집단으로 나눌 수 있는 조합의 수만큼 평균 차이를 검정할 수 있는 최소 조합 t-검정 방법을 제안하고자 한다. 최종적으로 본 논문에서는 한 개씩 추출된 표본들 사이의 이질성을 확인하기 위하여 평균 차이를 검정할 수 있는 방법을 제안하였고 모의실험 연구를 통해 성능을 확인하였고 실제 자료 분석을 통해 결과를 도출하였다.


Supported by : Chung-Ang University


  1. Dunn, O. J. (1961). Multiple comparisons among means, Journal of the American Statistical Association, 56, 52-64.
  2. Fisher, R. (1918). The correlation between relatives on the supposition of Mendelian inheritance, Transactions of the Royal Society of Edinburgh, 52, 399-433.
  3. Hochberg, Y. and Benjamini, Y. (1990). More powerful procedures for multiple significance testing, Statistics in medicine, 9, 811-818.
  4. Holm, S. (1979). A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics, 6, 65-70.
  5. Kruskal, W. H. and Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis, Journal of the American statistical Association, 47, 583-621.
  6. Marusyk, A. and Polyak, K. (2010). Tumor heterogeneity: causes and consequences, Biochimica et Biophysica Acta (BBA)-Reviews on Cancer, 1805, 105-117.
  7. Student. (1908). The probable error of a mean, Biometrika, 6, 1-25.
  8. Yoo, J., Kim, Y., Lim, C., Heo, M., Hwang, I., and Chong, S. (2017). Assessment of Spatial Tumor Heterogeneity using CT Phenotypic Features Estimated by Semi-Automated 3D CT Volumetry of Multiple Pulmonary Metastatic Nodules: A Preliminary Study, unpublished manuscript.