Test twenty true-null hypotheses at p<0.05 and you expect one ‘significant’ result from pure noise. Run enough tests and you can ‘discover’ anything. Slide (or tap) the correction from none to full Bonferroni and watch the false alarms go quiet.
With m independent true-null tests at threshold α, the chance of at least one false positive is the family-wise error rate FWER = 1 − (1−α)^m, and the expected count is m·α. At m=20, α=0.05 that is a 64% chance of a false discovery. The Bonferroni correction tests each at α/m, holding FWER ≤ α. The slider blends the threshold from α to α/m; a fail-loud self-check throws unless FWER falls from ≈0.64 to ≈0.05 across the sweep.
Independence of the m tests and a common α are the simplifying assumptions (real tests correlate; Bonferroni is then conservative, and Holm / Benjamini-Hochberg refine it); m=20 is illustrative. The 1−(1−α)^m and α/m arithmetic is exact.