DOI QR코드

DOI QR Code

An elaboration on sample size determination for correlations based on effect sizes and confidence interval width: a guide for researchers

  • Mohamad Adam Bujang (Clinical Research Centre, Sarawak General Hospital, Ministry of Health Malaysia)
  • Received : 2023.10.11
  • Accepted : 2024.01.04
  • Published : 2024.05.31

Abstract

Objectives: This paper aims to serve as a useful guide for sample size determination for various correlation analyses that are based on effect sizes and confidence interval width. Materials and Methods: Sample size determinations are calculated for Pearson's correlation, Spearman's rank correlation, and Kendall's Tau-b correlation. Examples of sample size statements and their justification are also included. Results: Using the same effect sizes, there are differences between the sample size determination of the 3 statistical tests. Based on an empirical calculation, a minimum sample size of 149 is usually adequate for performing both parametric and non-parametric correlation analysis to determine at least a moderate to an excellent degree of correlation with acceptable confidence interval width. Conclusions: Determining data assumption(s) is one of the challenges to offering a valid technique to estimate the required sample size for correlation analyses. Sample size tables are provided and these will help researchers to estimate a minimum sample size requirement based on correlation analyses.

Keywords

Acknowledgement

We thank the Director General Ministry of Health for permitting us to publish the paper.

References

  1. Pearson K. Notes on the history of correlation. Biometrika 1920;13:25-45. https://doi.org/10.1093/biomet/13.1.25
  2. Rodriguez RN. Correlation. In Kotz S, Johnson NL, editors. Encyclopedia of statistical sciences. New York, NY: Wiley; 1982. p193-204.
  3. Kendall M. A new measure of rank correlation. Biometrika 1938;30:81-93. https://doi.org/10.1093/biomet/30.1-2.81
  4. Bonett DG, Wright TA. Sample size requirements for estimating Pearson, Kendall, and Spearman correlations. Psychometrika 2000;65:23-28. https://doi.org/10.1007/BF02294183
  5. Moinesterm M, Gottfried R. Sample size estimation for correlations with pre-specified confidence interval. TQMP 2014;10:124-130. https://doi.org/10.20982/tqmp.10.2.p0124
  6. Bujang MA, Nurakmal B. Sample size guideline for correlation analysis. World J Soc Sci Res 2016;3:37-46. https://doi.org/10.22158/wjssr.v3n1p37
  7. NCSS, LLC. PASS 2022 Power Analysis and Sample Size Software. Kaysville, UT: NCSS, LLC.; 2022.
  8. Bujang MA, Adnan TH. Requirements for minimum sample size for sensitivity and specificity analysis. J Clin Diagn Res 2016;10:YE01-YE06. https://doi.org/10.7860/JCDR/2016/18129.8744
  9. Bujang MA, Baharum N. A simplified guide to the determination of sample size requirements for estimating the value of intraclass correlation coefficient: a review. Arch Orofac Sci 2017;12:1-11.
  10. Bujang MA. An elaboration on sample size planning for performing a one-sample sensitivity and specificity analysis by basing on calculations on a specified 95% confidence interval width. Diagnostics (Basel) 2023;13:1390.
  11. Young DS. Handbook of regression methods. Boca Raton, FL: CRC Press; 2017.
  12. Shrestha N. Detecting multicollinearity in regression analysis. Am J Appl Math Stat 2020;8:39-42. https://doi.org/10.12691/ajams-8-2-1
  13. Cohen J. A power primer. Psychol Bull 1992;112:155-159. https://doi.org/10.1037/0033-2909.112.1.155
  14. Belinda B, Peat J. Medical statistics: a guide to SPSS, data analysis, and critical appraisal. 2nd ed. Oxford: Wiley; 2014.
  15. El Hangouche AJ, Jniene A, Aboudrar S, Errguig L, Rkain H, Cherti M, et al. Relationship between poor quality sleep, excessive daytime sleepiness and low academic performance in medical students. Adv Med Educ Pract 2018;9:631-638. https://doi.org/10.2147/AMEP.S162350
  16. Ottaviani FM, Marco AD. Multiple linear regression model for improved project cost forecasting. Procedia Comput Sci 2022;196:808-815.
  17. Chu M, Nguyen T, Pandey V, Zhou Y, Pham HN, Bar-Yoseph R, et al. Respiration rate and volume measurements using wearable strain sensors. NPJ Digit Med 2019;2:8.
  18. Bujang MA. A step-by-step process on sample size determination for medical research. Malays J Med Sci 2021;28:15-27. https://doi.org/10.21315/mjms2021.28.2.2