Is he right?

Turnout has indeed been higher in Republican contests than in Democrat contests this year. That’s true in two ways. First, Republican contests this year are seeing more voters than Democratic contests in the same states. Second, compared to 2008 — when both parties had contested nominations — GOP turnout is up and Democratic turnout is down.

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But what about Trump’s second assertion? Will that surge in voters translate into a Republican victory in the general election? Many seem to believe that the answer is yes.

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The evidence hasn’t revealed a clear link

There has not been much scholarly study of how voter turnout in primaries affects the outcome of the general election, but the relationship appears quite tenuous. David Brooks recently argued on “Meet the Press” that “there is no correlation between primary turnout and wins in the fall in the last 11 elections,” a conclusion deemed “true” by Politifact.

Other analyses of the aggregate data also indicate primary turnout is unrelated to general election outcomes. Overall, the evidence suggest that it’s a mixed bag.

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The rush to declare that high turnout will be an advantage for the Republicans is especially tenuous in 2016.

First, as noted above, turnout in Democratic contests is being compared to 2008. That year was historic and exceptional. The party set records for voter participation in its primaries and caucuses.

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It looks as though Republicans are on track to set a new turnout record for the party this year. But Democratic turnout his year is not exactly low, coming in about where it was in the three nomination seasons before 2008.

For the primaries and caucuses that have taken place in 2016 for which we can get reliable data, Democratic turnout has been on average 10.7 percent, compared to 15.4 percent in the same states in 2008. For Republicans the picture is reversed: up to 14.7 percent in 2016 compared to 10.7 percent in 2008. If turnout were all that drove general elections, this would portend well for the GOP.

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GOP turnout isn’t necessarily all because of enthusiasm. Anxiety can motivate voters, too.

Second, and more important, it is a mistake to attribute all of the increase in Republican primary and caucus turnout to enthusiasm. Political science research has shown that political participation can be motivated by “enthusiasm” but also “anxiety.”

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Some primary voters surely turned out because they want Trump, just as he contends. But many others seem to be voting to stop Trump.

A recent Washington Post-ABC News Poll found that whereas three-fourths of Democrats would be “satisfied” with either Clinton or Sanders as the party nominee, none of the Republican candidates is viewed so positively by GOP voters. Trump fares worst, with only half of Republicans saying they would be satisfied with him as nominee.

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Compared to other Republican candidates, Trump isn’t viewed especially favorably. Among independents – the group that has helped to buoy turnout this year – he is viewed far more negatively than his fellows. This makes it difficult to believe that higher turnout now will be unambiguously good for the Republicans in November.

Trump does correctly state that more independents are voting in Republican contests this year. The figure below shows that Republican primary voters (the red dots) are especially independent in 2016. In states where we have data from exit and entrance polls, the share who called themselves independent was 27.6 percent in GOP primaries and caucuses but only 23.2 percent in Democratic contests.

But is that a huge difference? Let’s leave aside the possibility that some independents are voting out of fear rather than hope. Even so, that four-point gap isn’t tremendously meaningful. Back in 2008, the shares of independents voting in these same states were 21.8 percent in the Democratic primary and 21.5 percent in the Republican primary. That’s only a .3 percentage percent difference. And yet Obama thumped McCain in the general election.

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In just about every state, primary exit polls show that Trump is performing no better among independents than among Republicans. In some cases he does worse. This is certainly not the same as “growing the party.”