How do you decide whether a stock screen's result is real or just a lucky sample?

When a screen (say, low price-to-book combined with rising earnings) shows strong results over the last decade, the first thing I want to know is how many independent periods that actually covers. Ten years of monthly rebalancing gives 120 observations, but they are heavily overlapping in terms of the macro regimes they sample, so the effective sample size can be much smaller than it looks. I also find it useful to compare the screen against a base rate: what would a random selection from the same universe, with the same turnover and survivorship assumptions, have returned? Many screens look impressive until you notice the universe was built from today's index members, which quietly removes the companies that failed along the way. Where I'm less sure is how to set the threshold for "enough." Some people use a minimum number of trades, others use a statistical test with a multiple-comparisons correction, and the two can disagree sharply when you have tried dozens of variants. How do you handle the gap between a screen that passed your checks and one that merely looked good on the chart?