As the U.S. election campaign nears its climax, Donald Trump is amping up his claim that the failure of opinion polls to predict Britain's June vote to leave the European Union presages a similar surprise in his favor on Tuesday. While there are some lessons to be learned from the Brexit referendum, other conclusions aren't backed by the evidence.

The focus is on two types of voters. Unlikely voters, those who don't typically bother participating in elections, did turn out for the EU plebiscite, but weren't considered to have an influence in the polls. Shy voters, those reluctant to admit non-consensus leanings (the technical term is Social Desirability Bias), don't tell the truth to pollsters. Shy Brexiteers showed up at the British referendum itself but were invisible in the polls; shy Tories were blamed when the outcome of the 2015 U.K. election defied expectations for a split parliament.

So might a significant number of Trump supporters be invisible now, only to emerge at Tuesday's ballot to deliver a Republican victory?

There are certainly parallels between Trump's rise and the Brexit decision. Economic insecurity, concern about immigration and societal change, a backlash against what some view as out-of-touch elites and a desire simply to shake things up are common themes. Some demographic elements are also similar, with support for both Trump and Brexit strong among whites without college degrees.

What's more, some of those who dismiss the comparisons are doing so on false grounds. They argue that the U.K. polls were neck and neck, whereas U.S. polls consistently favor Clinton. Now, if you average the Brexit results over the entire campaign (as you might for an election), they were indeed 50/50. But if you look at the final polls (as you should in a referendum, where you'd expect a swing to the status quo as decision day neared), the mismatch between the polls and the outcome is much clearer.

In the U.K., there's evidence to suggest that social desirability bias was a factor in the 1992 election, but not in other cases. For example, the Conservative party in 2015 outperformed its polling in places where support was strongest, the opposite of what you'd expect if social pressures were an issue. The same is true of the June Brexit referendum.

In the U.S., if a shy Trump supporters bias was evident, you'd expect a divergence between internet and live caller polls. While there are several reasons why different polling methods might deliver different results, if shy voters were an issue then the difference ought to be significant. Instead, the gap is slight — and both internet and telephone surveys typically show Hillary Clinton in the lead.

Another crucial aspect of the Brexit plebiscite was a surge in turnout, boosting participation by about six percentage points compared with the 2015 election. Although research is still ongoing, the work done so far suggests that millions of people who typically don't participate in elections turned out to vote against the establishment.

That might seem to be an example of the so-called "missing white voters" Trump is hoping for. But if those absentees were planning to take part, they should already be showing up in the early voting data that states have been publishing. Instead, Clinton has what the New York Times called "a considerable lead" in North Carolina, for example, where something like 40 percent of the electorate has already cast its vote. There's a similar picture emerging in Nevada.

Finally, the Brexit campaign was helped because the majority of its backers displayed strong, coherent and consistent enthusiasm for their chosen side. Trump's core support is undeniably unwavering — witness his ability to shrug off gaffe after gaffe — but across the Republican bloc as a whole, there's a reluctance that, if anything, echoes the lackluster backing that typified the pro-European camp in the U.K. rather than the coherence of the victorious Brexiteers.

It would be foolish to dismiss the possibility that U.S. voters will spring a surprise on Tuesday. Nor should we assume it will happen, just because it could. But Trump supporters looking to the Brexit example for succor and support should be wary of drawing parallels that simply don't exist.

• Singh runs Number Cruncher Politics, a nonpartisan polling and elections site that predicted the 2015 U.K. election polling failure.