The study aimed to investigate the impact of count data on bivariate correlation coefficients, including Pearson's correlation coefficient, Spearman's rank correlation coefficient, and Kendall's correlation coefficient, particularly when the data follows bivariate binomial and Poisson distributions. The study considered sample sizes of 10, 20, 30, 50, and 100, with correlation levels of 0, 0.2, 0.6, and 0.8. The study compared the performance of the correlation coefficients based on their ability to control the probability of type I error and power at a significance level of 0.05. The simulation results indicated that when the data adhere to bivariate binomial and Poisson distributions, the Pearson correlation coefficient, Spearman's rank correlation coefficient, and Kendall's tau correlation coefficient effectively control the probability of a type I error. Furthermore, when assessing the power of a test at correlation levels of 0.6 and 0.8, the Pearson's correlation test statistics demonstrated the highest power across all scenarios, even with small sample sizes.
Chumnaul et al. (Tue,) studied this question.