Statistics

p-value

The probability of observing data at least as extreme as yours, assuming the null hypothesis is true.

P(data this extreme | null true).

The trap. It is not P(null true | data). Converting between them needs a prior and Bayes' theorem, and for an a priori unlikely hypothesis a p-value of 0.05 leaves it still probably false.

Multiple testing destroys it. Test 20 worthless strategies at the 5% level and one looks significant by construction. Backtesting is multiple testing: every parameter tuned and date range tried is another test. A strategy that survives 200 attempts is exactly what noise produces.

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Hypothesis Testing and p-values

What a p-value is and is not, why multiple testing destroys naive inference, and how that applies to backtests.

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