P-Hacking in Crime Investigations

The Problem of Multiple Testing #

Over the past twenty years we’ve become increasingly aware that repeatedly probing a dataset for various hypotheses will produce phantom findings. Ask the dataset enough questions, and eventually you’ll get lucky and stumble upon a false positive. The problem is that outliers discovered in this way are rarely reproducible; they don’t generalize.

Lets go with an example. Suppose I have a dataset of 100 surgeons, finding that surgeons are unusually likely to run red lights. 5% of the population have been ticketed for running a red light; 10% of our surgeons have been ticketed. We do a binomial test - “What is the likelihood that surgeons are ticketed at 5%, same as everyone else, and our dataset containing 10 bad apples is sheer luck?” The binomial test tells that if surgeons actually had the same 5% ticketing rate as the general population, the probability of observing 10 or more ticketed surgeons in a sample of 100 would be about 2.8% -> we pass a naive test for statistical significance.

The issue being, if we take our 100-surgeon dataset and ask it 1000 such questions, we will land in that 3% sheer-luck case several times, and we can produce dozens of shocking studies about the criminality of surgeons that way. This type of bruteforcing is one form of p-hacking.

One way to avoid p-hacking is preregistration - before a researcher is allowed to look at the data, they submit a list of the tests they want to run. Every additional test raises the bar; if we were testing the surgeons for five different types of crime and we made the exact same finding as before, we might say that the likelihood of getting lucky is no longer 3%, but rather 10% or 15% (suddenly a much flimsier finding, despite the observations being the same!)

P-Hacking for Detectives #

Lets apply the concept of p-hacking to criminal investigations, background checks, and mass surveillance. Consider a private detective out to find dirt on a politician. The actions of that detective have the same methodological issue as the p-hacking researcher. The detective combs over messages, public appearances, hand movements and clothing choices, searching for evidence of one type of misdeed. If nothing is found, he just moves to the next angle. At some point, you get lucky and find a false positive - an incorrect transcript, a moment of edginess or drunkenness, a falsely remembered witness testimony, a windfall that’s genuine luck but looks like corruption, a murder confession made in sarcastic jest or as part of a video game chat.

At this point, my chatGPT editor raises an objection:

The number of examples required doesn't scale directly with the amount of available data.

Imagine you have 20 years of someone's messages and find:

"I killed John. The body is buried under the oak tree."
along with independent evidence that John is dead and the body is actually under the oak tree.

An enormously unlikely piece of evidence doesn't become weak merely because you searched a large database.

And to that my answer is - the confession on its own is not an enormously unlikely piece of evidence. You can probably find many such confessions by attention-seekers. Feel free to dig up the oak tree and check; if you find something, the evidentiary weight will be mostly borne by that corroborating evidence, not merely by the verbal confession.

Anecdotes Don’t Scale #

There are also issues in treating anecdotes as data in a world of big data. Suppose we had an archive of every message you’ve ever sent - a treasure trove of incriminating data. At that scale, even a message that is beyond the pale should not suffice to condemn. Instead, you’d be looking for a strong pattern - many messages distributed across time. Analogy: finding ten murderous surgeons would be a very strong effect it came from a dataset with only a hundrd surgeons. The same ten murderers found in a dataset with millions of surgeons is a very weak effect size, likely not even above the base level.

As we enter an age of mass surveillance where there is far more data out there on each of us, the bar for establishing wrongdoing should also be raised in proportion. At a societal level, we have to understand that the more categories of wrongdoing there are, and the more data we can comb through to find such wrongdoings, the more likely it is to stumble onto false positives by chance. If an investigator is looking through 20 years of social media posts, they’d better be able to cough up thousands of examples, not dozens.

Raise the Bar #

In summary, the more things you search for, the less surprising it is that you eventually find something suspicious, and the less evidentiary weight any one suspicious finding should carry. A larger search space must result in much stronger evidence.