The human brain seems wired to notice patterns.  This presumably has some evolutionary advantages, but this attribute can lead us astray in a world that is overloaded with data.  I’ll start with a personal anecdote, and then show the implications for data analysis.

Back on June 18th, I was traveling through the west side of Vancouver and noticed a street name “Trutch”.  I recall thinking that this was an odd name.  Just a few days later, Tyler Cowen linked to an article in the Vancouver newspaper, discussing the fact that this street’s name had just been changed:

Vancouver’s Trutch Street is now šxʷməθkʷəy̓əmasəm Street. Not everyone is happy

Dan Fumano: Many residents of the street very recently known as Trutch said they support changing the name. But they worry about possible practical implications of a street whose sole name is spelled in a language other than English.

Author of the article:  By Dan Fumano  Published Jun 17, 2025, Last updated Jun 18, 2025

That’s an even odder name!

Notice that the name change occurred right about the time I observed the street.  That seems like a rather amazing coincidence.  But that’s not all.  This past Monday we stayed one night in a hotel in Calgary, before flying home.  The next morning I woke up and checked Marginal Revolution.  This is the first post that I saw:

Calgary is resuming with fluoride, and Quebec fact of the day

That’s even more of a coincidence.  It’s almost as if Tyler knew of my travel plans and intentionally posted material that related to my location.  Of course that’s nonsense, he didn’t even know I was on a vacation.  But you can see how a superstitious person might find the coincidences to be meaningful.  What are the odds?

Perhaps you are thinking that in a world where billions of events happen every single day, a coincidence isn’t all that meaningful.  But much of our research in science and social science is premised on the assumption that coincidences are very meaningful.  At least in physics, scientists often insist on highly unusual coincidences, “5 sigma events”, which means more than 5 standard deviations from the predicted value.  But in many fields there is a much weaker test of significance, just two standard deviations from the null hypothesis.  That means that random coincidences with just 20 to 1 odds against are viewed as highly meaningful.

In a recent EconLog post, Kevin Corcoran had this to say:

In 2007, Eliezer Yudkowsky wrote an interesting article advocating for what he called “defying the data.” The idea was fairly simple – say you have some theory explaining how the world works. A new study is published with data that can’t be accounted for with your theoretical framework. How should you respond?

One response is to abandon your theory in favor of the new data. Another response is to keep your theory intact and, as Yudkowsky says, “attack the experiment – accuse the researchers of dishonesty, or flawed design, or conflict of interest.” But there is a third possibility – that of simply defying the data. . . .

If a theory has been well-established and upheld by multiple studies and experiments, then one really striking appearance of contrary data shouldn’t amount to much.

At first glance, that might sound unscientific.  But in practice it is often the case that evidence “refuting” a given theory is nothing more than a garden-variety coincidence—something that happens every single day.

Even very smart pundits (and myself) are occasionally fooled by coincidences.  One of the worst recent examples involves the debate over the origin of Covid.  Throughout history, pandemics often begin in major cities in southern China, where large populations live in close proximity to wild animal markets.  This is how the first SARS epidemic began in November 2002.  The Covid pandemic (SARS-2) seems to have begun in an almost identical fashion, in a wild animal market in one of southern China’s largest cities.

Despite that fact, many pundits have embraced the completely unsubstantiated theory that Covid came from a lab leak, because among the half dozen largest metro areas in southern China, it first popped up in one that has an important virus research institute.  That’s one of the weakest coincidences I’ve ever seen, and yet many people seem to view it as providing strong support for the lab leak theory.  In contrast, the animal market hypothesis is based on a coincidence that is many orders of magnitude more unlikely to occur at random.

There are millions of streets in the world.  The fact that I noticed a certain street in Vancouver right before Tyler posted an article about that street is actually a pretty amazing coincidence.  And then for Tyler’s fluoride post to occur just 10 days later, just as I was passing through Calgary, is an even more amazing coincidence.  In contrast, the entire lab leak theory is based on nothing more than a mild coincidence that is about as interesting as rolling the same number two consecutive times when tossing a six-sided die.