The author evaluated the implications of nominal statistical significance for changing the credibility of null versus alternative hypotheses across a large number of observational associations for which formal statistical significance (p < 0.05) was claimed. Calculation of the Bayes factor (B) under different assumptions was performed on 272 observational associations published in 2004-2005 and a data set of 50 meta-analyses on gene-disease associations (752 studies) for which statistically significant associations had been claimed (p < 0.05). Depending on the formulation of the prior, statistically significant results offered less than strong support to the credibility (B > 0.10) for 54-77% of the 272 epidemiologic associations for diverse risk factors and 44-70% of the 50 associations from genetic meta-analyses. Sometimes nominally statistically significant results even decreased the credibility of the probed association in comparison with what was thought before the study was conducted. Five of six meta-analyses with less than substantial support (B > 0.032) lost their nominal statistical significance in a subsequent (more recent) meta-analysis, while this did not occur in any of seven meta-analyses with decisive support (B < 0.01). In these large data sets of observational associations, formal statistical significance alone failed to increase much the credibility of many postulated associations. Bayes factors may be used routinely to interpret "significant" associations.