NIST’s multiple-comparison framework explains why selecting the best result after many tests can make chance look like a discovery.

What the source establishes

NIST describes Bonferroni’s method for controlling a family of comparisons by allocating error probability across the specified set. The key point is that the collection of tests matters, rather than only the one result eventually highlighted. NIST/SEMATECH — Bonferroni multiple-comparison method ↗

For an explicitly illustrative set of twenty independent null tests, each with a 5% false-positive probability, the chance of at least one false positive is 1 minus 0.95 to the twentieth power, approximately 64.2%. Independence is part of this example; correlated tests require their own analysis.

What the distinction changes

An advertiser can make a backtest look impressive by showing only the best combination of indicator, expiry and date range. The omitted trials are part of the research process. Without them, the reader cannot tell whether the result was specified in advance or selected because it looked strongest.

Multiple-testing adjustment also cannot repair every weakness. A test with leaked future information remains defective even after an error-rate correction. The selection process and the information timeline require separate checks.

Questions for the next review

Record all candidate rules and selection criteria before evaluating a final holdout. Preserve unsuccessful tests in the research log. Describe a selected historical result as such, and avoid treating a nominal significance level as a probability that a trading strategy will make money.