Many commentators argue that the upcoming Brexit referendum in Britain, on membership of the European Union, could hasten the breakup of Britain. Scotland had a referendum only two years ago on whether it should leave the United Kingdom and become independent. Some pro-E.U. commentators have argued that the cause of Scottish independence might get a new breath of life if Britain leaves the European Union. Scottish voters, they argue, might feel a closer bond to Europe than to England, leading some people who voted no to Scottish independence two years ago to change their points of view. Scotland’s ruling SNP party might then run a new referendum and win it.

However, for this to be plausible, the pro-Scottish independence camp would have to keep together its existing coalition after Britain left the European Union, while persuading enough people who voted no on independence last time to change their vote to yes. Opinion survey evidence suggest that this may be difficult.

The Scottish electorate is divided on Europe

For years, Scottish politicians such as former prime minister Alex Salmond have argued that Scotland should look to the example of Ireland – an independent country that, until recently at least, did well by being part of the European Union. Such arguments have led to a general perception that people who want Scottish independence are also pro-Europe. This perception is mistaken.

An analysis of survey data from the British Election Study shows that people who voted for Scottish independence had mixed feelings about Europe and democracy. Some voters shared the cosmopolitan social democratic vision espoused by the leadership of the pro-independence campaign. Others did not.

We can distinguish at least four groups in the Scottish electorate. Civic nationalists, like the Independence campaign’s leadership, are pro-egalitarian, anti-austerity and unhappy with the state of democracy in Britain. Classic nationalists are not particularly concerned about issues such as austerity and income inequality, but do want independence. Labour Party loyalists (so named here because many of this group identify with the Labour Party) do not want independence, but do have some concerns about income inequality. Finally, traditional unionists are attached to the Union of Scotland and England, and also very conservative.

Both civic nationalists and classic nationalists voted overwhelmingly yes for Scottish independence, while Labour Party loyalists and traditional unionists voted no. The key question is whether a British exit from Europe would sway enough people who had voted no to Scottish independence to change their vote to yes, while avoiding defections from the yes camp to the no camp.

Many supporters of Scottish independence are anti-E.U.

Survey results suggest that classic nationalists are much less egalitarian and cosmopolitan than civic nationalists. Civic nationalists mostly see immigration as a good thing, while classic nationalists believe the opposite. Although civic nationalists in 2014 were highly likely to express an intention to vote in favor of remaining in the European Union, classic nationalists were the least likely of all four groups to do so. Further, classic nationalists, at 24 percent of the Scottish electorate, were more numerous than civic nationalists, who made up 20.5 percent at the time of the 2014 referendum. This suggests that a very substantial share of pro-Independence voters are actively skeptical of the European Union. This complicates the usual story that Scottish pro-independence voters would be mobilized by a British exit from the European Union.

Brexit may not persuade those who voted against Scottish independence to switch their vote

Those who voted against Scottish independence in 2014 were typically either Labour Party loyalists or traditional unionists. Labour Party loyalists are generally pro-European Union, suggesting that voters in this group might be persuaded by Brexit to move from a no vote to a yes vote. At the time of the 2014 referendum, Labour Party loyalists did not perceive immigration quite as positively as civic nationalists. But they did generally say they wanted the United Kingdom to stay in the European Union. In contrast, traditional unionists were the least likely of all groups to view immigration in positive terms and, on balance, said they preferred to leave the European Union.

But would enough Labour Party loyalists switch to the pro-independence camp in the event of Brexit?

Although members of this group are quite similar to civic nationalists across a number of issues, they were unwilling to support an orderly break from the United Kingdom under the relatively stable conditions in 2014. It is questionable that they would support a more disorderly exit under the conditions of Brexit. Further, these voters do not have a strong sense of Scottish identity. In fact, they are least likely of all groups to express a strong sense of Scottish identity.

The Labour Party has given this group of voters a way to express their solidarity with the rest of Britain, and their preferences on Europe have historically been secondary. Indeed, all four groups are somewhat skeptical about Europe – no group had a majority in support of pushing the E.U. project any further, while even some prominent civic nationalists have recently broken ranks with the SNP’s commitment to the European Union.

Getting to yes is a challenge

It is hard to see how a yes vote in the Brexit referendum would necessarily lead to a yes vote in any future referendum on Scottish independence. Voters who already favor Scottish independence are much less pro-Europe than believed. Voters who didn’t want Scottish independence in 2014 are unlikely to change their minds in large numbers solely on the question of Europe.

None of this completely rules out the possibility of Scottish independence after Brexit. The leading voice of the pro-independence movement, the SNP, has if anything grown in stature since the failed referendum of 2014, performing particularly well in last year’s general election. There are other complicating factors, too.

But E.U. membership is not necessarily the kind of touchstone issue for Scottish voters that many commentators believe it to be. Brexit is unlikely to immediately push a large majority of Scottish voters to demand an exit from the United Kingdom.

John Connolly is a statistician with the University of Texas at Arlington, and has a PhD in political science.