Monday, September 20, 2021

Heuristic: Insensitivity to Sample-Size

This is actually a cluster of heuristics and rather than tease them out individually I will give a few examples.


I shared with my sister-in-law, a retired, Registered Nurse, that I thought that the nurse who prepped me for my Colonoscopy was drunk.

She assured me that was impossible. "She is an RN. She cannot be drunk."

Her reasoning was that because she was an RN and she would NEVER show up to work under-the-influence that all RNs were immune to the possibility.

Regression-to-the-mean tells us that as the sample size gets larger it will drift toward the mean for the population regardless of what my sister-in-law wants to believe.

I had a similar encounter with an attorney. He simply could not believe that data showed that some sub-populations are more likely to commit violent crimes or engage in mass murders of people who do not belong to their sub-population. His argument was "I personally know one fellow lawyer from each sub-population and I refuse to believe what you are telling me."


From a distance, the crowd is dark gray. The Jumbtron inset shows that smaller samples is bright blue. People constantly see examples like this.

People expect small samples to "look" like the over-all population. This expectation persists in spite of ample evidence to the contrary.

Map of racial distribution in Los Angeles, 2010 U.S. Census. Each dot is 25 people: WhiteBlackAsian Hispanic.  Image by Erica Fischer

The City of Los Angeles, California is approximately 50% Hispanic, 30% non-Hispanic white, 10% Asian and 10% Black and yet there are many neighborhoods where nearly every household is Black, or Asian or Hispanic.

EVERYBODY KNOWS THIS. And yet, at a visceral level, we still expect small samples to look like the population was put through the Bass-o-matic and poured into a tumbler.

Homogenous/Heterogenous are concepts that are scale dependent.


People expect strings of random numbers/events to look "random" when, in fact, Heads-H-H-H-H-H-H-H is a perfectly random string of coin flips that comes up about once every thousand flips.

If the first eight flips are all Heads, then assuming the game is rigged is a reasonable assumption since there are 1023-of-1024 other equally-likely outcomes.

But if the string of eight Heads in a row occurs in the middle of a thousand flips, then that is not evidence of an unfair coin and at some point the absence of "strings" is evidence that the coin is rigged.

Mortality risk

Given very large samples, some people are going to die in strange ways.

The Detroit Metro area has a population of about four million people. The 90 people who die in bed every 24 hours is never newsworthy but the guy who got his head stuck in the storm-drain and drowned (he had dropped his keys) is newsworthy. 

Because the storm-drain death made the news soccer moms KNOW they are death-traps, just like plastic bags, five-gallon buckets and wildflowers.

In a similar way, a drug-dealer gets into a shoot-out with the cops and a stray round hits his girlfriend/business partner. It makes the news. Everybody now "knows" that cops are blood-thirsty brutes who shoot some people on-sight.

And cities burn.

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