In the past couple of weeks British number-lovers and data journalists have all been analysing the Scottish referendum. First using polls to try and predict the results and, now that the votes have been counted, looking at who voted which way to try to identify patterns.

Here at Figure It Out we’ve been watching closely ourselves, each for different reasons. Some of us are Scottish, others have spent years living north of the border and others still are deeply interested in the political ramifications of the vote.
We thought, then, that it was time for us to look at the numbers behind this most momentous of independence votes and some of what we found is interesting indeed.
During the live coverage relationships between the demographics of the electorate in each Scottish council and the voting results for that council were identified and we thought we’d take a look for ourselves. We decided to take categories that could be influencers separately and look to see if areas where more people fall into those categories are also areas where more people voted yes.

To do this, we used a mathematical tool called “correlation”, which finds the line that passes through a plot of two data-sets such that the sum of the distances of every data point from the line is the smallest of every possible line through those data-points. (This is an optimisation problem all on its own).

Correlation explanation

The probability that this line represents a relationship between the two sets of data is then calculated, with a score of +1 meaning that they are exactly related, 0 meaning that there is no relationship at all and -1 meaning that they are inversely related, which in this case would mean a perfect relationship with a “No” vote rather than a “Yes” one.

Just looking at BBC’s map of who voted what shows a couple of likely contender categories for a relationship:
BBC voting map
It appears that “No” votes are stronger near the English border and “Yes” votes stronger in the inner cities (at least, Glasgow and Dundee).
So we looked at these categories first, using Scottish census data from 2011 to inform us about the demographics of each council ward.

Throughout all of the following charts, the below colour key is used:
article colour key

National identity

It turns out that areas with a higher proportion of people who identify as purely English are moderately more likely to have voted “No”, whilst conversely (and linked), people who identify as purely Scottish are moderately more likely to have voted “Yes”. There is no impact at all on voting tendencies for areas that have a larger proportion of people who do not claim any UK national identity.
national identity correlation with Yes vote
In this case, the strongest result is actually that the proportion of the electorate with no UK national identity didn’t have any correlated relationship to a vote either way – a correlation coefficient of almost exactly zero suggests that there was no impact at all, although some parts of Scotland have quite a high number of non UK residents (as much as 12% in Aberdeen and 11% in Edinburgh). It’s unsurprising that areas with more native Scots voted for independence and areas with more native English (max 6% in Dumfries and on Orkney) voted against.

Urban vs Rural

There is only a weak relationship between the proportion of people living in rural areas and the vote. People living in more urban wards were slightly more likely to vote “Yes”:
urban proportion compared to Referendum "Yes" vote
After considering these relationships, we turned to another possible “obvious” indicator for how an area would vote – the way in which they voted in the last Westminster election.

Westminster election vote 2010

Very interestingly here, contrary to what we would have assumed, the proportion of votes for SNP was not the strongest relationship to voting tendency of each of the political parties. Nor was it the second, or even third strongest.
Correlation between 2010 Westminster vote and 2014 Referendum vote
The strongest relationship between the 2010 vote and the referendum vote was the 2010 vote for Labour (2010 voting data taken from electoral calculus), having a moderate link to a 2014 “Yes” vote. A tendency to vote for the SNP in 2010 was the least closely related of the four main political parties, with only a weak correlation.

Then finally we looked at a variety of economic indicators.

Council spending

The amount that councils spend per capita turns out to be unrelated to the way in which the electorate chose to vote (data from
Scottish spend per capita compared to referendum "Yes" vote


Unemployment rate, however, is correlated to the vote. Regardless of how long people have been unemployed, the areas with higher unemployment had a higher tendency to vote “Yes”. This relationship is stronger in areas where unemployment is longer term.
Correlation between unemployment rate and referendum vote

Level of education

There are only weak correlations between people’s level of education and the way that they chose to vote,although there is a demonstrated link between earnings and education which might have indicated that since unemployment is moderately correlated to “Yes” voting then education level would also have been.
Correlation between education level and Scottish referendum vote
The weaker link with education level shows a slight tendency for people with no qualifications to vote “Yes” and for those with degree level qualifications to vote “No”. As education level is linked to earnings / employment, this is a relationship that would typically be ignored in favour of the stronger relationship with unemployment so we can’t conclude that the “No” vote is also the educated vote.

Type of work

We only found two moderate relationships between work type and voting tendency. People who are small employers or responsible for their own businesses were more likely to vote “No” and people in intermediate occupations (see here for detailed definition of Scottish census occupation classifications) were more likely to vote “Yes”.
Correlation between social class and Scottish referendum vote
What we found most interesting in this whistlestop tour of what prompted who to vote which way is that we didn’t find any strong relationships between voter demographics and the way that they voted in the referendum.  There are, however, several moderate relationships:

  • Areas with more unemployed people were moderately more likely to vote “Yes”
  • Areas where more people who identified themselves as solely English live were moderately more likely to vote “No
  • Areas with more small employers were moderately more likely to vote “No”
  • Areas with a higher Labour vote were moderately more likely to vote “Yes”
  • Areas with higher Conservative or Liberal Democrat votes were moderately more likely to vote “No”
  • Areas with more people in intermediate occupations were moderately more likely to vote “No”

There’s nothing here that suggests that a single factor could have been used to predict the votes in any of the council wards, but there are certainly plenty of relationships to keep people talking for a while.