Significance (5% FDR)
A result unlikely to be chance alone, after allowing for how many were tested at once.
Test three hundred pairs at the usual 5% and about fifteen look significant by luck. The false-discovery-rate adjustment raises each p-value to a q-value so that, among everything flagged, at most one in twenty is expected to be a false alarm. Significance says a difference is unlikely to be noise; it says nothing about cause, and nothing about whether the relationship will continue.
Formula
q(k) = min over j ≥ k of p(j) × m ÷ j (p sorted, m tests)
How to read it
Flagged when q is below 0.05.
In Kereon
Charts · Correlation. Benjamini–Hochberg, within each family on screen: every pair's test of one kind, or every change along one rolling chart. Correlation ≠ 0: Student's t (Pearson, Spearman) or the normal approximation (Kendall). A change, a difference from history or between normal and stressed markets: two independent correlations compared by Fisher's z. Returns cluster in size, so these are approximations.
Also called: significance, q-value, q value.