The Dumb Statistical Argument in Texas’s Election Lawsuit

These claims rocketed around the Twittersphere yesterday (citations removed):

Expert analysis using a commonly accepted statistical test further raises serious questions as to the integrity of this election.

The probability of former Vice President Biden winning the popular vote in the four Defendant States — Georgia, Michigan, Pennsylvania, and Wisconsin — independently given President Trump’s early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000. For former Vice President Biden to win these four States collectively, the odds of  that event happening decrease to less than one in a quadrillion to the fourth power (i.e., 1 in 1,000,000,000,000,000).

The same less than one in a quadrillion statistical improbability of Mr. Biden winning the popular vote in the four Defendant States — Georgia, Michigan, Pennsylvania, and Wisconsin — independently exists when Mr. Biden’s performance in each of those Defendant States is compared to former Secretary of State Hilary Clinton’s [sic] performance in the 2016 general election.

The statistical details are from an expert declaration available here, and they’re about as silly as you would expect.

Basically, the exercises simply assume that different batches of ballots should have similar breakdowns by candidate or party. If Biden got more support than Clinton had, or if late-counted ballots were more heavily Biden-leaning than early ballots, that’s treated as evidence of fraud. And the statistical tests are incredibly emphatic that these differences are real — one in a quadrillion! — because of the enormous sample sizes, including millions of ballots.

But you can’t prove that Biden did better than Clinton had because of fraud simply by showing that . . . well, Biden did better than Clinton had . . . and it’s not surprising at all that late-counted (mainly mail-in) ballots were more Democratic than earlier ballots.

You don’t have to take my word for it. The declaration itself describes the hypotheses it’s testing as whether “the percentages of the votes Clinton and Biden achieved in the respective elections are similar” and whether “the reported tabulations in the early and subsequent periods” could plausibly be “random samples from the same population of all Georgia ballots tabulated.” (The declaration starts with Georgia and then repeats the process for the other states.)

The two candidates obviously did not perform similarly; one won and one lost. Early and late ballots are not simply random draws from the overall collection of ballots. And that implies nothing about fraud.