The best replacement for pearson correlation is spearman.

The best alternatives to pearson correlation are rated as following:
★★★★★  spearman
★★★  spearman rank
★★★  t test
★★★  r squared
★  chi square
★  spearman correlation
★  euclidean distance
★  cosine similarity
★  spearman rho
  covariance
  t-test
  icc

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pearson correlation
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