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Notes on Statistics

REMAIN %

LEAVE %

Yougov poll results for the last 38 polls

The re-weighted data is shown as thick red lines (negative percentages for Leave, positive percentages for Remain). 

Original YouGov data shown as thin blue lines.  These are about 2% lower, on average, than the adjusted data.

The green line is a regression on the adjusted data and the black line a regression on the YouGov data. 

Note that the green line is slightly steeper than the original and is shifted up by about 2%.

 

1. THE ADJUSTMENT

 

The headline percentage difference provided by some of the polling organisations (particularly YouGov) have been adjusted, in this study, to take account of

 

(a) the fact that some (particularly YouGov polls) only sample from Great Britain, not the UK (which includes Northern Ireland) plus Gibraltar.

(b) YouGov undertake their survey asking individuals what social group/voting group/age group etc., they belong to.   They then weight the poll so that it corresponds to the national demographics.  For example, if they asked 1000 people whether they supported the reintroduction of grammar schools, but the sample they asked turned out to be 100 Labour voters and 900 Conservative voters, they would have to divide the answers given by the Conservative voters by 9 if the national demographic were that the same number voted Labour as voted Conservative. 

 

Polling companies publish their target weights (see section 2 below) but those target proportions for the remain/leave/did-not-vote do not always correspond to the actual UK+Gib proportions at the referendum.  Partly this is due to (a) but that only has a minor effect.  The adjustment here is to undo their weightings and then re-weight the polls so they exactly correspond to the proportions at the referendum.

 

HOW IS THIS DONE?

 

The weights in YouGov, for instance, under weigh the 'did-not-vote' group.  Yougov uses 18%, the actual figure is about 28% non-voters.  The calculation is simple. 

 

The figures typically come in the structure shown.  Figures in black are typically supplied by the poll.  Figures in red are calculated from the black or from other figures in red.  The bottom two rows, for example, simply apply the percentages given in the polls to the actual votes at the referendum.  The polls do not give the 'did not vote' percentage, but that can be deduced from all the other figures in the poll, as shown below, and then applied to the number of electors who chose not to vote.

 

You can put your own figures in and see the outcome using the button to recalculate.  Figures shown are as truncated integers but actual calculations use real numbers, so totals will not be exact due to rounding errors.

 

Select from the YouGov polls:  or put in your own figures

 

  TOTALS Voted Remain at the  referendum Voted Leave at the referendum Did not vote TOTALS Majority Percentage
Actual UK/Gib total votes  

16,141,241

17,410,742

 12,913,178=12,958,258 minus number of spoilt ballots

     
WEIGHTED GB SAMPLE      
Right to LEAVE % % %      
Right to REMAIN % % %      
Don't know/Prefer not say. % % %      
               
Numbers from the sample that would vote LEAVE now        
Numbers from the sample that would vote REMAIN now        
               
Applied to actual referendum figures: LEAVE        
Applied to actual referendum figures: REMAIN      

 Note that the majority is for  and the majority amongst those who did not vote was % for   

2. UNHELPFUL POLL WEIGHTINGS

YouGov, for instance, use the following poll target percentage weightings (see, for instance page 8 on April 13th poll):

EU referendum Vote (Election Result)

Target percentage weightings used in BMG UK poll Oct 2016

(only two polls in the study are from BMG)

Target percentage used in all YouGov weightings

(30 polls in study are from YouGov)

  Actual UK+Gib referendum votes Actual UK+Gib percentage
Remain  32.6%  39.3%   16,141,241 34.7%
Leave 35.9% 42.7%   17,410,742 37.5%
Don't Know / Did Not Vote 27.2% 18.0%   12,913,178 27.8%

BMG and YouGov figures are shown in blue, actual voting figures shown in black

It can be seen that YouGov target weighting percentages over-weight the voters (Remain and Leave rows) and underweight the 'did not vote/don't know' group.  This has the effect of giving (a) an apparent (but not real) greater majority for Remain than is the case: 42.7% - 39.3% = 3.4% (or 4.14% just amongst voters) majority by comparison with 37.5% - 34.7% = 2.8% (or 3.8% when just amongst voters, which was the actual winning margin) and (b) given the 'don't know/did not vote' group has a strong majority (currently running at about 20%) in favour of Remain, YouGov will only be including 18% of that, and not 27.8%.  i.e. they will not be including that contribution as much as it should be included, which diminishes the poll count for Remain.  Overall the effect of these weights is to report a significantly diminished Remain majority.

The BMG weightings, by comparison (green highlights above) which are for the UK (but excluding Gibraltar), correspond much more closely to the actual referendum percentages.  Note they do not add up to 100 because some will not have answered the question and they have been given a weighting in the BMG poll.

The adjustments made in the presentation of the results using the scheme in section 1 above, reverse that YouGov under-reporting.  Averaged over the 30 polls, the under reporting is just under 2%, so, for example, where YouGov says that leave and remain are equal on 44%, the figures are more likely to be 43% in favour of leaving and 45% in favour of remaining.  Obviously that would provide a significantly different referendum result.

A comparison of weightings is shown at the top of the page.  The Yougov basic differences are shown as thin blue lines, about 2% lower, on average, than the adjusted data.  The green line is a regression on the adjusted data and the black line a regression on the YouGov data.  The green line is slightly steeper than the original and is shifted up by about 2%.

3. THE NORTHERN IRELAND and GIBRALTAR ELEMENT

The YouGov polls do not include Northern Ireland or Gibraltar in their polling.  They voted to remain by about 120,000 (combined).  The polls (mostly only GB), nevertheless, have been implements on the total UK number so the calculation will generally be an underestimate of the Remain vote.  Whilst the majorities are small (of the order of 1%-2%), to do the calculation accurately would be within the noise of the poll, but a rough estimate could be made by, simply, adding 120,000 to the REMAIN majority which is approximately an extra 0.3%.

4. CLAIM THAT THE CURVE REPRESENTING THE LEAVE MAJORITY IS MARGINALLY INCREASING

The entry 'marginally increasing' is based on (a) the very good linear (and polynomial) fit to the two data sets (non voters from last time) on the third graph which implies that the majority is increasing and currently at about 18% (and increasing) whilst (b) the number of  new 18 year old voters is about 750,000 per year, which a similar number of deaths, mostly over 65.  The 18-24 group saw a majority for Remain of about 75% whilst the over 60's were about 35% for Remain.  Assuming people stick to their votes (as is indicated in the polls with about 90% on both camps sticking to their votes), then there is a new electorate of about 32,000 (=40% of 80,000) per month in favour of Remain.  Over a year, given turnout rates etc., that corresponds to approximately 150,000 more remain votes and 250,000 less leave votes.  That will mean a small but increasing majority for Remain.  One study by the Financial Times puts the tipping point even if no abstainers vote, at the end of 2021. I think it much earlier than that, indeed we may have already passed that point, see here.

5. DASHBOARD

There is a dashboard in which you can test scenarios as to when the voters (ignoring - or not - the non-voters) would comprise new 18 year-olds who would, according to the polls, overturn the simple vote.  Of course, if there were a referendum tomorrow, the polls comprehensively suggest that Remain would win by more than 1 million. 

6. THE 12.7 MILLION

More Remainers than Brexiteers failed to vote on June 23rd.  That is almost certainly related to the pre-polling expectation that Remain would win, so there was more complacency amongst the remain voters.  A similar effect may have put Trump in place in the USA and there are a number of studies which demonstrate that effect (see articles referred to the in main web page for references).