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A new approach to constructing confidence intervals for population means based on small samples

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  • Hao-Chun Lu
  • Yan Xu
  • Tom Lu
  • Chun-Jung Huang

Abstract

This paper presents a new approach to constructing the confidence interval for the mean value of a population when the distribution is unknown and the sample size is small, called the Percentile Data Construction Method (PDCM). A simulation was conducted to compare the performance of the PDCM confidence interval with those generated by the Percentile Bootstrap (PB) and Normal Theory (NT) methods. Both the convergence probability and average interval width criterion are considered when seeking to find the best interval. The results show that the PDCM outperforms both the PB and NT methods when the sample size is less than 30 or a large population variance exists.

Suggested Citation

  • Hao-Chun Lu & Yan Xu & Tom Lu & Chun-Jung Huang, 2022. "A new approach to constructing confidence intervals for population means based on small samples," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-17, August.
    • Handle: RePEc:plo:pone00:0271163
    DOI: 10.1371/journal.pone.0271163
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    2. Peddada, Shyamal Das, 1997. "Confidence interval estimation of population means subject to order restrictions using resampling procedures," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 255-265, February.
    3. Harris, R. I. D. & Judge, G., 1998. "Small sample testing for cointegration using the bootstrap approach," Economics Letters, Elsevier, vol. 58(1), pages 31-37, January.
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