The logic of the Bonferroni correction for multiple tests, or family-wise error, is to set the criterion to reduce the expected number of erroneous false positives, or Type I errors, below 1. This is a very stringent criterion for false positives in cases where the test may be applied millions of times, and will necessarily introduce a large proportion of false negatives (missed positives, or Type II errors). A proposed solution to this problem is to adjust the criterion for False Discovery Rate (Benjamini & Hochberg, 1995), which allows the number of false positives to increase proportionally to the number of true positives, though remaining at a small proportion, dramatically reducing the number of false negatives. This approach may be conceptualized as working with a relaxed confidence level that any one test is a true rather than a false positive, bringing the criterion more into line with our societal assessment of the validity of statements in general, and even in science, as having less than 100% certainty. The analytic strategy to the assessment of statistical significance provides a more intuitive approach to the identification of sparse signals in large datasets than the standard Bonferroni approach to correction for multiple tests.
Christopher W. Tyler, "Rational Approaches to Correcting for Multiple Tests" in Proc. IS&T Int’l. Symp. on Electronic Imaging: Human Vision and Electronic Imaging, 2018, pp 1 - 8, https://doi.org/10.2352/ISSN.2470-1173.2018.14.HVEI-535