Multiple Testing refers to the statistical problem arising when performing multiple hypothesis tests simultaneously on the same dataset. In crypto trading and quantitative finance, this occurs when backtesting numerous trading strategies, searching for profitable patterns across many cryptocurrencies, or evaluating the significance of multiple market signals. The core issue is that conducting multiple tests inflates the probability of encountering false positives, leading to spurious discoveries or strategies that appear effective purely by chance.
Mechanism
The mechanism of inflated false positives is statistical: even if all null hypotheses are true, there is always a non-zero probability of incorrectly rejecting a null hypothesis (Type I error) for any single test. When many tests are conducted, these individual probabilities accumulate, significantly increasing the overall probability of making at least one Type I error across the set of tests. This effect can lead to misleading conclusions about the efficacy of a strategy.
Methodology
Addressing multiple testing involves employing specific statistical methodologies to control the error rate. Common approaches include controlling the Family-Wise Error Rate (FWER) using methods like the Bonferroni correction or Holm’s method, which adjust the significance level for each individual test. Alternatively, controlling the False Discovery Rate (FDR) using methods like Benjamini-Hochberg is often preferred in exploratory analyses, as it is less conservative and controls the expected proportion of false positives among all rejected null hypotheses.
A strategy's viability is not determined by its backtested performance, but by the quantifiable probability that its discovery was not a statistical illusion.
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