Field experiments testing the effects of online ads on political candidates and issues have also found null effects. We shouldn’t be surprised — it’s hard to change people’s minds! Their votes are shaped by fundamental factors like which party they typically support and how they view the state of the economy. “Fake news” and bots are likely to have vastly smaller effects, especially given how polarized our politics have become.

Here’s what you should look for in evaluating claims about vast persuasion effects from dubious online content:

How many people actually saw the questionable material. Many alarming statistics have been produced since the election about how many times “fake news” was shared on Facebook or how many times Russian bots retweeted content on Twitter. These statistics obscure the fact that the content being shared may not reach many Americans (most people are not on Twitter and consume relatively little political news) or even many humans (many bot followers may themselves be bots).

Whether the people being exposed are persuadable. Dubious political content online is disproportionately likely to reach heavy news consumers who already have strong opinions. For instance, a study I conducted with Andrew Guess of Princeton and Jason Reifler of the University of Exeter in Britain showed that exposure to fake news websites before the 2016 election was heavily concentrated among the 10 percent of Americans with the most conservative information diets — not exactly swing voters.

The proportion of news people saw that is bogus. The total number of shares or likes that fake news and bots attract can sound enormous until you consider how much information circulates online. Twitter, for instance, reported that Russian bots tweeted 2.1 million times before the election — certainly a worrisome number. But these represented only 1 percent of all election-related tweets and 0.5 percent of views of election-related tweets.

Similarly, my study with Mr. Guess and Mr. Reifler found that the mean number of articles on fake news websites visited by Trump supporters was 13.1, but only 40 percent of his supporters visited such websites, and they represented only about 6 percent of the pages they visited on sites focusing on news topics.