Reminder: statistical outliers are not prima facie evidence of untoward behavior.
I've seen several posts alleging fraudulent behavior in this election based on anomalous voter turnout numbers. These numbers are outside the norm and are "statistically impossible" and therefore must be fraud. But a couple of things to keep in mind:
- Demand curves slope downward. As costs fall, quantity demanded increases. The broad push and relaxation of mail-in voting rules in this election reduced costs for many voters. So, ceteris paribus, we would expect a greater number of votes cast. Couple this fact with the contentiousness of the election and the apocalyptic predictions of defeat on both sides, and it's likely the demand curve shifted out. Falling costs and increasing demand would produce more quantity demanded.
- If there is little variation in the data, then even a small change (in absolute terms) from the mean could be multiple standard deviations from the mean. For example, let's say we have a voting area where, for the past 6 elections, voter turnout has ranged from 66.2%-66.4%. The standard deviation here is 0.089. Thus, even an increase in voter turnout to 66.5% would represent a statistically significant increase. Something like 66.7% would be far outside the "normal." But these fairly small increases wouldn't be much of an increase in voting numbers in absolute terms (depending on the underlying size of the population, an increase of 0.5 percentage points could simply be one extra family voting!).
Likewise, of course, the absence of statistical anomalies doesn't mean there is no untoward behavior. The lack of a gender gap between male pay and female pay in the marketplace once accounting for various differences in career, education, and the like does not imply no gender discrimination.
Folks love to point to anomalous behavior and cry foul. We see it with global warming, COVID, discrimination, and the like. Unfortunately, we are now seeing it with voting. But remember: just because something looks mathy, doesn't mean it's reasonable or scientific. It is far more likely mere truthiness and scientism. One needs theory. Facts never, ever, speak for themselves.