A p-value is the probability of obtaining a result at least as extreme as the one observed if the strategy truly has no real edge.

A p-value is the probability of obtaining a result at least as extreme as the one observed if the strategy truly has no real edge. In strategy validation, that makes the p-value a measure of how surprising a backtest outcome would be under a null hypothesis of no skill or no predictive power. A small p-value means the observed result would be less likely to appear from randomness alone. It does not mean the probability that the strategy works, and it does not directly measure economic value or robustness across future data.[1]

In Sonar’s strategy-validation research, the p-value is used to frame statistical significance around a backtest result. The logic is hypothesis testing. First define a null hypothesis that the strategy has no edge. Then measure the observed statistic from the backtest. Then ask how often a result at least that extreme would appear if the null hypothesis were true. The p-value is that tail probability.[1]

In the backtest-overfitting audit tool, the p-value is tied to the audit’s resampling and benchmark logic. The tool evaluates whether the observed strategy outcome is distinguishable from outcomes that could arise without a genuine edge. The computation compares the observed result with a distribution generated under a no-edge framework, and the p-value is the fraction of null outcomes that are as extreme as or more extreme than the observed backtest result. This makes the p-value a diagnostic for whether apparent performance may be statistical noise rather than evidence of a persistent signal.[2]

This is also why the p-value should be interpreted carefully in quantitative research. It answers a narrow question about extremeness under the null. It does not answer the inverse question that many researchers instinctively want to ask. A p-value does not tell you the probability that the null is true. It does not tell you the probability that the strategy will hold up live. It is one layer of evidence in a broader validation process.[1][2]

The deflated Sharpe ratio plays a related but distinct role. Sonar’s glossary describes the deflated Sharpe ratio as an adjustment to Sharpe ratio significance that accounts for non-normal returns, short samples, and multiple testing. That matters because a raw Sharpe ratio can look impressive even when many variants were tried or when return distributions violate ideal assumptions. The deflated Sharpe ratio addresses the chance that an apparently strong Sharpe ratio is inflated by selection effects or distributional artifacts.[3]

Compared with the p-value, the deflated Sharpe ratio is more specific to risk-adjusted performance and the practical distortions common in strategy research. The p-value asks whether the result is unusually extreme under a no-edge null. The deflated Sharpe ratio asks whether an observed Sharpe ratio remains statistically credible after adjusting for features that can exaggerate significance. Both tools help separate true edge from statistical noise, but they do so from different angles. The p-value is a general hypothesis-testing probability. The deflated Sharpe ratio is a correction framework for evaluating Sharpe-based evidence in realistic research settings.[1][3]

For a quantitative trader or research analyst, the key point is conceptual discipline. A p-value quantifies how surprising a backtest result would be if there were no real edge. That is useful because it helps distinguish signal from randomness. But it is not a direct probability that the strategy works, and it should be read alongside tools such as the deflated Sharpe ratio when judging whether apparent performance reflects genuine information or statistical noise.[1][2][3]

Covered in depth in the Strategy validation & overfitting pillar hub.