REQUIRED SAMPLE SIZE FOR CORRELATION ANALYSIS

Sample size calculation prior to data collection is still relatively rare in Russian research practice. This situation threatens validity of the conclusion of many projects due to insufficient statistical power to estimate the parameters of interest with desired precision or to detect the differences of interest. Moreover, in a substantial proportion of cases where sample size calculations are performed simplified formulas with assumption of a normal distribution of the studied variables are used in spite of the fact that this assumption does not hold for many research questions in biomedical research. Correlation analysis is still one of the most commonly used methods of statistical analysis used in Russia. Pearson’s correlation coefficient despite its well-known limitations appears in a greater proportion of publications that non-parametric coefficients. We calculated minimal sample sizes for the parametric Pearson’s coefficient as well its non-parametric alternatives — Spearman’s rho and Kendall’s tau-b correlation coefficients to assist junior researchers with the tool to be able to plan data collection and analysis for several types of data, various expected strengths of associations and research questions. The results are presented in ready-for-use tables with required sample size for the three abovementioned coefficients within the range from 0,10 through 0,90 by 0,05 for statistical power 0,8 and 0,9 and alpha-error or 5% as well as for estimation of the same correlation coefficients with the 95% confidence intervals width equal to 0,1 and 0,2.

marine medicine, Sample size, statistical power, correlation analysis, Pearson’s coefficient, Spearman’s coefficient, Kendall’s coefficient

1. Grjibovski A.M. Correlation analysis. Human Ecology, 2008, No. 9, pp. 50–60 (In Russ.)].

2. Kholmatova K.K., Grjibovski A.M. Ecological Studies in Medicine and Public Health. Human Ecology, 2016, No. 9, pp. 57–64 (In Russ.).

3. Guenther W.C. Desk Calculation of Probabilities for the Distribution of the Sample Correlation Coefficient // The American Statistician. 1977. Vol. 31 (1). Р. 45–48.

4. Devroye L. Non-Uniform Random Variate Generation. New York: Springer-Verlag, 1986.

5. Gardner M.J., Altman D.G. Confidence intervals rather than P values: estimation rather than hypothesis testing // Brit. Med. J. (Clin. Res. Ed.). 1986. Mar. 15; Vol. 292 (6522). Р. 746–750.

6. Amrhein V., Greenland S., McShane B. Scientists rise up against statistical significance // Nature. 2019. Vol. 567 (7748). Р. 305–307.

7. Bonett D.G., Wright T.A. Sample Size Requirements for Estimating Pearson, Kendall and Spearman Correlations // Psychometrika. 2000. Vol. 65 (1). Р. 23–28.

8. Looney S.W. Sample size determination for correlation coefficient inference: Practical problems and practical solutions // American Statistical Association. 1996. Proceedings of the Section on Statistical Education. Р. 240–245. 9. Cook R.D., Weisburg S. Applied Regression Including Computing and Graphics. John Wiley and Sons Inc., 1999.