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

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

doi:10.1371/journal.pone.0271163

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

PLoS One. 2022 Aug 17;17(8):e0271163. doi: 10.1371/journal.pone.0271163. eCollection 2022.

Authors

Hao-Chun Lu^{1

2}, Yan Xu³, Tom Lu⁴, Chun-Jung Huang⁵

Affiliations

¹ Department of Management Science, National Yang Ming Chiao Tung University, Hsinchu, Taiwan.
² Graduate Institute of Management, Chang Gung University, Taoyuan, Taiwan.
³ School of Mathematics, Ocean University of China, Qingdao, China.
⁴ Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, United States of America.
⁵ Fab12 Manufacturing-1 Department, Taiwan Semiconductor Manufacturing Company, Hsinchu, Taiwan.

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.

Publication types

Research Support, Non-U.S. Gov't
Retracted Publication

MeSH terms

Computer Simulation
Confidence Intervals
Models, Statistical*
Probability
Research Design*
Sample Size

Grants and funding

Funding: The first author HCL was supported by the Ministry of Science and Technology of Taiwan under the Grant MOST 110-2410-H-182-008-MY3. YX was supported by the National Natural Science Foundation of China (no.12026239). Taiwan Semiconductor Manufacturing Company provided support for the study in the form of salary for CJH. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.