search for


Reliability coefficient for weighted sum of variables
Journal of the Korean Data & Information Science Society 2024;35:207-15
Published online March 31, 2024;
© 2024 Korean Data and Information Science Society.

Hyeonah Park1 · Seongryong Na2

12Division of Data Science, Yonsei University
Correspondence to: 1 Lecturer, Division of Data Science, Yonsei University, Wonju 26493, Korea. E-mail:
2 Professor, Division of Data Science, Yonsei University, Wonju 26493, Korea.
Received February 23, 2024; Revised March 11, 2024; Accepted March 12, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
When the observed score consists of a true score and an error, the reliability coefficient is expressed as the ratio of the variance of the true score to the variance of the observed score. This observation score is a construct and can be explained as a simple or weighted sum of variables that are subconstructs. Cronbach’s alpha is the lower limit of the reliability coefficient derived from a simple sum of variables. This research proposes a reliability coefficient with internal consistency derived from a weighted sum of variables. Through simulation experiments using virtual and real data, the impact of adjusting weights or removing variables on reliability is explained using the existing Cronbach’s alpha and the proposed reliability coefficient.
Keywords : Construct, Cronbach’s alpha, reliability, weighted sum