I'm looking for any statistical tool to use instead of the Pearson correlation coefficient. In fact, My purpose is finding a more effective tool than this to use in data sets.
1) If your data meet the parametric criteria, you should use a parametric correlation coefficient.
2) Non-parametric coefficients are Kendall tau rank or Spearman's rank correlation (Here a tutorial for Kendall correlation https://bit.ly/2yeqiWX)
3) If your data are dichotomous (zeros and ones) you could test the Phi coefficient. This article explains about that.
https://www.jstor.org/stable/1302424
(See an application in this article Table 3 https://ulinx.org/CuqyC)
4) However, one of the most robust techniques for measuring the degree of association between two sets of data, (regardless of whether the data meet parametric assumptions) is the coefficient of C, proposed by Gregorius (2007).
I've used it in various papers (It's my preferred method).
Gregorius, H. R., Degen, B., & König, A. (2007). Problems in the analysis of genetic differentiation among populations-a case study in Quercus robur. Silvae Genetica, 56(1-6), 190-199.
The disadvantage of this method is that there is no R library to run it. In case you need to use this method, send me your data and I will return the results to you (I use a C-language script to run it). The interpretation is similar as the other coefficients.