Former secretary of state Hillary Clinton acknowledges the audience as she arrives onstage to sign copies of her new book “What Happened” at Barnes and Noble bookstore on Sept. 12 in New York City. (Drew Angerer/Getty Images)

With the release of Hillary Clinton’s campaign memoir last week, political observers have turned their attention back to the 2016 presidential race.

And that, inevitably, leads to James Comey. A central debate in the campaign post-mortems is whether Comey, then the FBI director, tipped the election in Donald Trump’s favor with the Oct. 28 release of a letter announcing the review of possible new evidence in the Clinton email investigation. Some journalists, political analysts and Clinton herself contend that the letter’s release cost her the presidency. “Absent that,” Clinton told NBC last week, “I believe the evidence shows I would have won.”

In a recent paper, however, we cast doubt on the claim. Using an analysis of polling data from the last four months of the campaign, we find no conclusive evidence that the Comey letter led to a decisive shift in voter support. Instead, changes in support for the candidates resulted largely from other factors.

Here’s how we did our research

We arrive at this conclusion through an analysis of Clinton and Trump’s standings in national polls from July 1 through the day before the November election. We use data from Pollster’s 2016 General Election poll chart. Specifically, our measure is Clinton’s share of the two candidates’ support.

We use time-series analysis to trace changes in the polls. Our statistical model accounts for economic conditions and presidential approval, which political scientists call campaign “fundamentals” because they are systematically associated with support for the incumbent party. We also include variables to capture the effects of the party conventions, the three presidential debates, as well as the volume of each candidate’s media coverage. (Details of the analysis appear in the paper.)

We measure the effect of the Comey letter by including a variable to examine changes in the polls on Oct. 28 — the day the letter was released — and in the days afterward. If the letter hurt Clinton, we should find a statistically significant decline in her lead over Trump, above and beyond what the other variables would tell us. This is a standard way of measuring whether a campaign event has a durable effect on the polls.

The turmoil surrounding former FBI Director James Comey and President Trump started long before Comey was fired on May 9. Here are the pivotal moments from Comey's time as head of the agency, including his private meetings with the president. (Jenny Starrs,Julio Negron/The Washington Post)

These three events clearly did affect Clinton’s lead

But that’s not what we find. Our model shows that the Comey letter led to a small drop in Clinton’s lead, but that shift is not statistically significant. In other words, there is no clear evidence that the letter cost Clinton votes. When we specify our model in different ways — for example, looking at the impact for just the three days after its release — we again do not find evidence that the letter moved the polls.

It is worth noting that we also find no indication that the release of the “Access Hollywood” tapes, in which Trump bragged about his sexual exploits with women, had an effect. What mattered most was President Barack Obama’s approval rating — when it went up, so did Clinton’s support — and the Democratic National Convention and the first presidential debate. Both of those increased Clinton’s lead in the polls.

Our analysis has some limitations

There are, of course, limitations to the analysis. We have relatively few observations (130 days), which means that there is likely to be statistical uncertainty associated with any variable, including the Comey letter’s release. That will necessarily make it harder to find “significant” effects.

In addition, our measures of media coverage don’t account for the tone of coverage toward Trump and Clinton. That means we can’t determine whether the Comey letter might have had an indirect effect on voter support by making the news about Clinton more negative.

But an analysis by the Shorenstein Center at Harvard University found that the tone of media coverage was similar for Trump and Clinton during the last three months of the campaign. As a result, the measure of the volume of coverage in our model may be just as useful as a direct measure of tone.

Finally, our data set of national polls doesn’t allow us to determine whether small effects from the Comey announcement (or other campaign events) might have mattered in states such as Pennsylvania, Wisconsin and Michigan, where Trump’s margin of victory was very small. That is worth additional scrutiny.

But based on the evidence at hand, we see no reason to conclude that the Comey letter produced shifts in Clinton’s support that were sizable, persistent or consequential.

Costas Panagopoulos is a professor of political science and director of Big Data and Quantitative Methods Initiatives at Northeastern University, and author of “Political Campaigns: Concepts, Context and Consequences” (Oxford University press, 2016). Find him on Twitter @professorcostas.

Aaron Weinschenk is an associate professor of political science at the University of Wisconsin at Green Bay and co-author (with Costas Panagopoulos) of “A Citizen’s Guide to U.S. Elections: Empowering Democracy in America” (Routledge, 2015). Find him on Twitter @aaronweinschenk.