To find out what lifestyle choices may cause kidney cancer, a study conducted by Howard Wainer and Harris L. Zwerling observed the rates of kidney cancer in every county in the United States. A clear pattern emerged: “The counties in which the incidence of kidney cancer is lowest are mostly rural, sparsely populated, and located in traditionally Republican states.”
A multitude of explanations spring up upon analyzing these areas. These rural counties have less air and water pollution, water pollution, greater access to unprocessed foods, and less access to alcohol.
Complications arises, however, upon considering which counties have the highest rates of kidney cancer. These areas are also mostly rural, sparsely populated, and located in traditionally Republican states.
How can the same description for counties with the lowest rates of kidney cancer also apply to counties with the highest rates of kidney cancer? Well, the answer may lie in the sparseness of population density.
Since the populations in these counties are small, they extreme statistical outcomes are more likely in any study. There is no significant underlying reason that causes the differentiating kidney cancer rates; it’s simply because small sample sizes increase the likelihood of outliers.
The same principle can help us make better evaluations of NFL teams early on in the season. When teams start out hot, we hear stories and stats about why the team is performing so well. Maybe the quarterback and his star receiver finally built up a rapport, or the team finally adapted to the coach’s new playbook, or the new roster additions are exceeding everyone’s expectations. Everyone looks for a reason to explain a team’s performance, just as Wainer and Zwerling searched for correlations to explain rates of kidney cancer in the counties described earlier. But much of it might be explained through the theory of randomness in which correlations don’t align in any way with causation.
As we just learned, small sample sizes produce extreme outcomes, and through just three weeks, we have a small sample size of the 2019 NFL season, and should expect there to be extreme outcomes so far.
Last year after three weeks, the Buccaneers, Broncos, and Bengals were 2-1, the Dolphins 3-0, and the eventual Super Bowl champion Patriots were just 1-2.
This year, the Lions, Bills, and 49ers remain undefeated to date. But are they legitimate contenders? The Chargers, Eagles, and Browns are all 1-2 out of the gate despite high expectations. Can they turn it around?
It’s tough to say. All we know for sure is that every year we overreact to the first few weeks and ignore the potential randomness of the causes of surprising outcomes. Let’s try to withhold judgment for as long as we can and avoid making the same mistakes this year. Proceed with caution; it’s a long, winding road ahead.