Analyses that test nonzero correlations and incorporate prior information can help accumulate knowledge and advance research at a faster pace than typical analyses that disregard previous studies and continue to test unreasonable nil hypotheses. The performance of several bootstrap and parametric procedures are evaluated using populations that had varying degrees of correlation and nonnormality. With correlated heteroscedastic variables, the parametric procedures produced robust point estimates, but showed liberal error rates that worsened as sample sizes grew to NObs = 1,000. This paper proposes two Bayesian univariate sampling bootstrap procedures (the SlotHI and SlotOI) that exhibit much better error rates across all evaluated populations and prior distributions. Based on this simulation, we suggest that the univariate sampling bootstraps are preferred when testing nonzero correlations in nonnormal populations, regardless if prior information is considered.