Which test do I use to estimate the correlation between an independent categorical variable and a dependent continuous variable?

Is it a fair assumption that if you do an Anova or Kruskal Wallis test with an independent categorical variable and a dependent continuous variable that shows no significance, to assume that there is no "correlation" between the two variables? For two continuous variables you can perform a Pearson or Spearman's correlation test, but I am not sure to use which test in the above mentioned situation?