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Quantopian Lecture Series: p-Hacking and Multiple Comparisons Bias

Multiple comparisons bias is a big problem in quantitative analysis. Effectively it's just the notion that the more tests you run, the more likely you are to get false positives (things that look like they confirm your hypothesis, but are really just random chance). If you don't correct for this at some point you're very likely to accept hypotheses that aren't based on any real relationships. p-Hacking is just the abuse of this phenomenon, in which someone runs tons of tests until they find one specific situation in which their tests pass. It can be intentional or inadvertent, but it happens. This lecture will introduce you to the concept, show some experimental examples, and talk about correcting for it.

All of our lectures can be found here:
www.quantopian.com/lectures.

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p-Hacking can also be explained as follows:

"All lies and jests Still a man hears what he wants to hear
And disregards the rest"
- Simon and Garfunkel, 1969

Disclaimer

The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.

Bonferroni is overly conservative as noted in the lecture, but Holm-Bonferroni is a good next step, and has an obvious application to pipeline. If we are doing a statistical test on all stocks in our universe, what is the significance level we should use to say an individual stock is above a cut off. Holm-Bonferroni suggests ranking and a formula for the cut-off. Does this make sense?

https://en.m.wikipedia.org/wiki/Holm–Bonferroni_method

This seems interesting! It definitely looks like a good improvement on the original Bonferroni correction (and I like that there's a proof on the Wikipedia page). An overall more powerful test is compelling.