A Statistical Framework for Evaluating the Fair Election Hypothesis

Everyone who taken a course in statistics has run into this, a seeming distinction without a difference. We look at data and find it does not sufficiently contradict the null hypothesis, H0. So we fail to reject H0. Ok, you say, good, so that means we accept H0. But not so fast. We don’t accept H0. It is not proved. We have only failed to disprove it. At this point, you may be justified in threatening to strangle me if I don’t stop this doubletalk, but hear me out. This is the crux of hypothesis testing in Statistics.

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Caleb Mars 2020

To take an example, consider a scenario in which we don’t have enough evidence to say a coin is unfair at the level of significance we desire. That doesn’t mean we are certifying it is fair. Suppose the coin turned up heads 8 times out of 10. That seems more than a tad suspicious. However, there is a 5.5% chance of getting a result as extreme as 8 or higher under the null hypothesis, H0, that the coin is fair. We would write H0: p=0.5 where p is the underlying probability the coin turns up heads. Our alternative hypothesis is , HA: p>.50. In words, the alternative is one-tailed scenario in which the coin is biased toward turning up heads. If we had chosen a 5% significance level (95% confidence) beforehand as our standard, we would fail to reject the null hypothesis that the coin is fair at that level of significance.

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Caleb Mars 2020

What does this have to do with stolen elections? Let’s adopt the null hypothesis the election was fair. Many Republicans want to reject that assumption on the basis of strong suspicions about the apparent vulnerability of the electoral processes in some states to voter fraud. Changes in procedure in several states have led to record turnout for a candidate who didn’t hold large rallies. Live unsolicited ballots were sent out to dead people and people who had moved. Ballot harvesters deposited hundreds of ballots in unguarded voting boxes. Signature verification and witness verification standards are alleged to have been greatly relaxed. There are depositions and videos of ballots in suitcases being pulled out after poll watchers were forced to leave the counting room. Some of the changes in electoral procedure may be in violation of the law. Further, depositions have been filed alleging various infractions, from counting late ballots to double-counting and rigging voting machines to have extra Biden votes. However, so far, none of these have led courts to overturn posted electoral results. Legal procedure includes processes such as Discovery and Interrogatories that could in theory turn up more evidence, but, in practice, time may be too short for the procedures to produce concrete evidence that meets the standard of proof required in a court.

So it appears there is not enough evidence to reject the null hypothesis that the election was fair. It is at point that legions of Mainstream Media pundits then declare this proves the election was fair. Not so fast. The failure to reject the null hypothesis that the election is fair at the necessary legal standard of proof does not mean we accept it as true. We can say we don’t have enough to prove widespread voter fraud. But as Statistics tells us that is not the same as accepting as proven the null hypothesis it was fair.

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politifact.com

So nearly half of a half of the voters may go on thinking the election was stolen and unfair, but they lack the evidence to prove it to the desired or necessary degree of significance. On the other hand, that doesn’t mean accepting as gospel the assertion the election was fair. The best that can be said at the current time is that we have failed to reject the null hypothesis the election is fair.

Mathematician, Statistician, Businessman, and Academic. Student of history, poli sci , and the Bible.

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