Some times you just want to put your hand on somebody’s shoulder and say in a sad and weary voice: “Just stop, you are embarrassing yourself”.
Surrounding the current state of affairs in the US Presidential election are various Trump supporters (including some Trump supporters who claim they aren’t Trump supporters) crying “fraud”. The evidence they have produced is so thin that they are often retracting bits of it themselves but claiming that the shear volume of BS that they have produced demonstrates that the claims must be true.
Amid that is the word “statistically”. Here is an example. An article by “Scott Hounsell” in RedState. It has fewer of the more blatant attempts at fake fraud claims but instead attempts to throw a cloud of suspicion over the election. Note the use of the word “statistically”:
“Additionally, turnout in 2016, as a percentage of registered voters, was just 79.80%. This year, the state jumped to a statistically impossible 92.26%, a 12.46% increase over their 2016 numbers. In a state when Democrats statistically lost more voters than Republicans, we are supposed to believe that a 12% increase (largest ever) swung majority to Dems, by a factor that not only overcame the margin by which Trump won the state in 2016 but also erased any gains Republicans had in registration (by losing less) and gave Biden a 20,000 vote lead?”https://redstate.com/scotthounsell/2020/11/05/excuse-me-while-i-call-bs-n275572
Fair enough, that paragraph does have statistics in it but quite what the writer thinks the word “statistically” is supposed to add (other than BS) is unclear. And “statistically impossible”? What on Earth is “statistically impossible” supposed to mean? I was already getting annoyed with seeing “statistically improbable” being thrown around on dodgy Facebook pages but at least those words made some sense.
A figure by itself is just a figure. If we are talking about the probability of an actual piece of data then “statistically” i.e. within the methodology of the discipline of statistics, we are comparing that figure with some model of the figures — for example an existing distribution derived from a theoretical understanding of the figures and/or past experience. The US election figures are boringly unremarkable. Turn out is up but outcomes aren’t very different from 2016. That’s the context and that doesn’t point towards data being “statistically impossible” but if you are going to invoke the djinn of statistics then you invoke what comes with it. To claim a figure is “statistically improbable” then you need to show that STATISTICALLY i.e. show that when compared to some valid model that the figure would only very rarely appear UNLESS some key assumption about the model was violated (eg massive fraud). Simply saying “statistically” a lot doesn’t make a number dubious, that’s just magical thinking.