After the 2020 US presidential election Donald Trump refused to concede, alleging widespread and unparalleled voter fraud. Trump's supporters deployed several statistical arguments in an attempt to cast doubt on the result. Reviewing the most prominent of these statistical claims, we conclude that none of them is even remotely convincing. The common logic behind these claims is that, if the election were fairly conducted, some feature of the observed 2020 election result would be unlikely or impossible. In each case, we find that the purportedly anomalous fact is either not a fact or not anomalous. © 2021 National Academy of Sciences. All rights reserved.