Peer-reviewedCC BYJournal of statistical theory and practice
Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine
- 1University of Chicago Laboratory High School, Chicago, IL, 60637 USA.
- 2School of Data, Mathematical, and Statistical Sciences, College of Sciences, University of Central Florida, Orlando, FL 32816 USA.
- 3Office of Biostatistics Research, Division of Intramural Research, National Heart, Lung, and Blood Institute, NIH, Bethesda, Maryland, USA.
Abstract
Small sample sizes in clinical studies arise from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the normal distribution approximation. In this paper, we employ a quadratic-form-based statistic, from which we derive more accurate confidence intervals, particularly for data with small sample sizes or proportions. Based on the study, we suggest reasonable values of sample sizes and proportions for the application of the quadratic method. Consequently, this method enhances the reliability of statistical inferences. We illustrate this method with real medical data from clinical trials.
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BibTeX
@article{wu2026confidence,
title = {{Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine}},
author = {Mulan Wu and Mengyu Xu and Dong-yun Kim},
journal = {Journal of statistical theory and practice},
year = {2026},
month = jun,
doi = {10.1007/s42519-026-00579-y},
url = {https://doi.org/10.1007/s42519-026-00579-y},
note = {CC BY},
}
RIS
TY - JOUR
TI - Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine
AU - Mulan Wu
AU - Mengyu Xu
AU - Dong-yun Kim
PY - 2026
DA - 2026/06/18
JO - Journal of statistical theory and practice
DO - 10.1007/s42519-026-00579-y
UR - https://doi.org/10.1007/s42519-026-00579-y
AB - Small sample sizes in clinical studies arise from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the normal distribution approximation. In this paper, we employ a quadratic-form-based statistic, from which we derive more accurate confidence intervals, particularly for data with small sample sizes or proportions. Based on the study, we suggest reasonable values of sample sizes and proportions for the application of the quadratic method. Consequently, this method enhances the reliability of statistical inferences. We illustrate this method with real medical data from clinical trials.
SN - 1559-8608
SN - 1559-8616
ER -