mardi 28 juin 2016

Brexit: why and how were we misled? The modes again


Since Friday, besides being angry at not forecasting the likely results, I ask myself how come. I thought that this required further analysis. What about modes?

Well, the difference between modes is one clear reason why I -- and others, I guess -- were misled. Contrary what we were expecting based on previous referendums and elections, the Web polls' estimates of the Leave side -- that we could call the "status quo ante" side -- were higher than telephone polls' estimates. As we can see in the following graph, during the campaign, web opt-in polls tended to put "Leave" at 50%. Telephone polls' estimates were way behind at the beginning of the campaign-- five points lower -- and around two points lower at the end.  On average, taking into account change over the campaign, web polls tended to put the Leave side 3.3 points higher than telephone polls.

However, there is substantial variation between estimates at the end of the campaign. Some web polls estimated support for Leave as high as 55% before Jo Cox's death and as low as 45% after. A similar situation exists for telephone polls: after estimating an advantage to Leave before Jo Cox's death, estimates went under the 50% line following her death. On average, in the polls, Jo Cox's death is followed by a drop of 2.9 points in the support for Leave.

Three conclusions arise from this analysis. First, the Web polls generally gave a better estimatation of the situation than telephone polls. We tended to believe that Web polls generally give higher estimates of the more liberal side (like in the Scottish referendum of 2014, in the UK 2015 general election and in many Canadian elections). However, in the US presidential campaign of 2012, web polls tended to produce lower estimates for Obama than telephone and IVR polls (see here). We may now conclude that Web polls generally give different estimates during the campaign but that they are not necessarily always biased in the same political direction.

Second, it is possible that people who were for Leave were even less likely to say so after Jo Cox's death. In short, maybe Jo Cox's death did not influence the vote but only the tendency to reveal a vote for Leave. This would give weight to the idea that social desirability -- or the Spiral of silence -- played a role in this campaign and that it was the Leave side who tended to hide its preferences.

Third, and very importantly, in the UK, it is the third time in a row -- Scotland 2014, UK 2015, Brexit 2016 -- that the estimates from the different modes differ substantially during the campaign but converge to similar average estimates at the end. This is mind boggling. I know that some researchers and pollsters explain it by "herding" but there is no proof of that, quite the reverse in fact. Although averages tend to be similar, there is much variation in estimates at the end of the campaign. It would be unlikely that pollsters using the same mode agree on an average! In France in 2002 (see Durand et al., 2004), I was informed by some pollsters on how they "chose" the published estimates. It would be "interesting" to get some insider information in the British case also.

With a non-proportional attribution of non-disclosers

Now, when I attribute 67% of non-disclosers to the Leave side, like I did in my last post and like I should have done all along, the web polls estimates show the Leave side ahead during all the campaign. On the opposite, the telephone polls did so only at the end. With this non-proportional attribution however, both modes give a very good estimate of the final vote, although some pollsters fared better than others.

In conclusion,

Pollsters conduct polls and their estimates are published in the media. The role of researchers is to analyze the polls and inform on their likely bias. However, when bias is not systematic, it is very difficult to do so. We need to understand when and why polls go wrong, and when and why there are differences in estimates according to mode of administration. However, in order to do so, we need to know where the numbers we are working with come from and how they are compiled, weighted and adjusted. Since polls may influence the vote in some situations, maybe poll data of published polls should be made available to researchers during electoral campaigns. Sturgis et al.'s analysis of the UK 2015 polls is a good example of what can be done when researchers have access to the data

vendredi 24 juin 2016

Brexit: we should have known better


Well, Quebec voted no to leave Canada, Scotland, no to leave UK and then UK leaves the EU. It is a bit ironic when you see it from Quebec, although Europe is not a country per se.

So what happened?

I am not sure that pollsters failed that much. However, I think analysts -- and I include myself -- failed. And I know how and why I failed. At the beginning of the campaign, a colleague of mine, Henry Milner, told me that it may be that, in this referendum, the status quo side was the Leave side. His argument was that older people tended to vote Leave, that they were raised in a country that was outside the EU and they may want to go back to "normality".

So what is the consequence in terms of analysis? The "Law of even polls" -- which states that when it is equal, status quo or the more conservative side is likely to prevail -- still applies...but you ought to know which side is status quo! I should have known better. I amend my law, adding this by-law: If you want to know which side is status quo, look at how older people vote. They are the ones who win elections. People between 18 and 34 years old form less than 20% of the population and an even lower proportion of the voters.

So, here is the graph that I get when I attribute 67% of non-disclosers to the Leave side instead of the Remain side (the reverse of what I have done so far).  I get a perfect prediction of the results.

In conclusion

A number of analysts, journalists, pollsters noticed during the campaign that older people clearly favored the Leave side. This should have rung the bells and led us to conclude that, in a very close situation, the Leave side was likely to win. In my case, I should have listened and attributed two thirds of the non-disclosers to the Leave side instead of Remain. With this procedure, the prediction is perfect.

jeudi 23 juin 2016

Brexit, an update that changes things a bit


I was not supposed to update unless there was some substantial change. Since yesterday, we added 10 new polls, i.e., those who were published since Tuesday and the Survey Monkey polls that were on the lists that we had consulted.

With these new polls, the situation is somewhat different.

The first graph shows change over time, with non-disclosers. It shows that there is a tendency towards a decrease in the proportion of non-disclosers (mostly undecideds). It also shows clearly now that the tendency is towards an increase in the support for Remain.

The second graph shows the estimates when non-disclosers are attributed proportionally. Even with this type of allocation, support for Remain is now ahead of Leave.

The final graph shows even more clearly that the Remain side is ahead of Leave. With this allocation, all the polls give a majority to Remain except one that puts the two sides at par. And the gap between the two is now estimated at 4.5 points.


With these new results, it is possible to conclude that the fatal shooting of Jo Cox probably had an impact on the campaign. It is rather clear from the second graph that most of the polls before the shooting gave an advantage to the Leave side and, on the contrary, most polls carried after give an advantage to Remain. If we look at the last graph that uses non-proportional allocation of non-disclosers, it is less clear, but nonetheless, the only estimates that gave a majority to Leave were before the shooting. More sophisticated statistical analysis will allow to validate -- or not -- this conclusion.

With these new results, we may conclude that Remain is likely to end up with a clear advantage of at least four points. Like everybody, I am eager to see the final results.

P.S. Thanks to Luis Pena Ibarra who recuperated the data and did most of the graphs for this campaign.

mercredi 22 juin 2016

Brexit, the day before


In this last analysis before election day, I use only the polls that were conducted during the campaign, i.e., from April 15 to June 20. If new polls were published since then, it may hardly change much what we see now. However, if there are such polls, I may update this message during the day. I first look at change in support overall and then, I look at the different portraits traced by the two modes of administration, i.e., telephone and web opt-in.

Change in support

The first graph shows the estimates of the different pollsters. It shows that the two sides are very close to each other. It also shows that the proportion of non-disclosers -- including undecideds and those who say they will not vote for pollsters who keep them in the samples -- is quite stable. However, this proportion varies much between pollsters -- from 3% to 26% -- so that it is not appropriate to look at the estimates of remain and leave without attributing these non-disclosers so that the proportions of Remain and Leave add up to 100%.

The next graph shows change over time when non-disclosers are attributed proportionally to each side for each poll. This is the procedure used by all pollsters, except for one recent BMG telephone poll. I will go back to this question later on. The portrait that emerges is that the positions have "crystallized" since the end of May. Since then, support for leave appears to be somewhat higher than support for remain. One also has to notice that the ceiling was reached not after the shooting of MP Jo Cox, but much before.

It is interesting to point out that the same situation occurred in Scotland for the referendum on independence. You can see in my last post of that campaign that support for both sides had also reached a ceiling close to 50% in the last weeks of the campaign. However, In Scotland, it was slightly more favourable to the status quo.

However, what Scotland -- and Quebec 1995 -- also show is that a proportional attribution of non-disclosers is likely to overestimate support for change. For example, in Scotland, a non-proportional attribution of 67% to the No side gave an estimation that was still a few points lower than the results of the referendum. You can see this analysis in my post Scotland, the day after.
I used the same non-proportional attribution of non-disclosers for the Brexit. One pollster, BMG Research, used the same attribution for its telephone polls (not its web polls). The pollster states that it asked a number of questions (which ones, we don't know) that led to conclude that this allocation was the appropriate one. You may look at the BMG report here. In addition, this post by Elections, etc. shows that polls almost always overestimate change.

The following graph shows the likely change in support over time using non-proportional attribution. Remain appears to be about two points ahead of Leave. In fact, with this allocation, there was only a short period last week where Leave was ahead of Remain. The last polls tend to show Remain ahead, at least when we use non-proportional attribution of non-disclosers.

By mode

Is the portrait traced by the two modes of administration the same? Not exactly. The next two graphs show the portrait of change over time in support for Remain, using either proportional or non-proportional attribution of non-disclosers. The two graphs show that the portrait is not the same according to mode. They both show also that telephone polls tended to estimate support for Remain five points higher than web opt-in polls at the beginning of the campaign but this discrepancy was reduced to two points at the end. With proportional attribution, telephone polls estimate support for Remain at 50%, opt-in web polls at 48%. With non-proportional attribution, the respective estimates are 52% and 50%. This means that the global estimates depend in part on the proportion of Web versus telephone polls that are conducted, so that weighting according to mode of administration -- like Number Cruncher does -- is not a bad idea.


It is interesting to notice that, as with the Scottish 2014 or the Quebec 1995 referendum, the Change side had momentum during the campaign but it  reached a ceiling in the last two weeks (or the last few days in the Quebec case). It seems clear that referendum campaigns do make a difference. I leave it to political scientists to analyse why and how it does.

The fact that the two modes of administration do not give the same estimates, not only of the level of support but also of change over time, is problematic. It is even more problematic since often, in small markets, the only polls that are conducted are web opt-in polls. We will see tomorrow which mode  led to better estimates. But nonetheless, there is an urgent need for research on ways to improve samples and estimates of polls if we do not want polls to mislead voters.

Will Remain win tomorrow? Like many others (see Elections, etc, for example), I think that it will. First, I think a non-proportional attribution of non-disclosers is more realistic and appropriate than a proportional attribution. Second, my own analysis is that the "Law of even polls" applies, i.e., when polls' estimates show two sides at par, the status quo side is likely to win, as it was the case in recent elections (Israel, UK, for example). If Remain does not win, I will have to modify the Law to take into account exceptions and figure out why this campaign was an exception, at the end.

I will have a last post on Friday to compare estimates and results.

Au plaisir

mardi 14 juin 2016

Brexit: It's all about modes?


We are close to entering the last week of the campaign. I will present an update of my last week analysis but, for this post, I will mainly focus on the major differences between modes.

First an update

As we can see in this first graph, the progression of the leave side went on during last week. However, it is important to notice that the Stay side remained stable. Its support did not decrease. What happens in that the progression of the Leave side seems to come almost entirely from a decrease in the proportion of respondents who say that they don't know how to vote or that they will not vote. This proportion, as noticed in a previous post, varies substantially, from3% to 15% during the last week.

If we attribute non-disclosers -- i.e. don't knows and will not vote -- proportionally like all the pollsters do, we get the following graph. We see that support for Leave has now pass support for Stay, as others have shown.

However, as I explained in preceding posts, empirically it is much more sound to attribute non-disclosers non proportionally, attributing more of them to the status quo side, in this case, Stay. If I keep the same non-proportional attribution that I used before -- 67% to stay and 33% to leave -- I get the following portrait of the situation. Support for Stay is slightly ahead of support of Leave, by about three points (it was five points last week).

However, it is very relevant to ask whether the portrait traced by polls is the same for telephone and Web opt-in polls.

It's all about modes

The first question is whether there is a difference between modes, controlling for change over time. In order to check for that, I perform a regression. The conclusions are:
  •  As we can easily see with the form of the curves in the preceding graphs, change over time is in the form of a reverse U (quadratic).
  • For Stay with proportional attribution of non-disclosers, after taking into account change over time, web polls give on average 5.1 points less to Stay than telephone polls. The mode, by itself, explains 45% of the variation between polls (which is huge!).
  • Using non-proportional attribution, the difference between modes is slightly corrected. Support for Stay in Web opt-in polls is 3.66 points lower on average than in telephone polls and mode explains 26% of the variation between polls.
 The second question is whether the two modes trace the same portrait of change over time. The simple answer is no. The first graph shows chance in support for Stay with proportional attribution of non-disclosers according to mode. It shows that, while telephone polls have estimated a steady decrease in support for Stay since the beginning of 2016, the web opt-in polls trace quite a different portrait. Is is only recently that they show a small decrease. These quite different portraits however converge to a similar estimate -- close to 50% -- in the last few days. The same thing happened in a way in the Scottish referendum where the difference between modes disappeared in the last weeks before election day.

If we use non-proportional attribution of non-disclosers, the portrait is similar but the endpoint estimate is slightly different, at 51.5%. However, since non-proportional attribution corrects for some of the differences between modes, there is no difference left in estimates according to mode.


Although the polls using different modes of administration do not trace the same portrait of change in support over time, it seems that, at the end, they tend to agree. So, as of now, we do not have to start a battle on who's right.

It seems to me that referendums on "independence" somewhat look alike, if one compares Quebec 1995, Scotland 2014 and the actual Brexit. During the campaign, the "change" side always gains support and, in the days before election, comes close to 50 percent . In Quebec and in Scotland, the "Law of even polls" was respected. This is, when the two sides are at par, the status quo side is likely to win. Why is that? We may speculate. It is possible that people who are for status quo tend less to reveal their preferences to pollsters or are less present in the samples. It is also possible that some people who are in favour of change are afraid of what could happen if change win by a tiny margin. they may therefore change their minds at the last minute. Anyhow, it is easier and less consequential to tell a pollster that you are going to vote for change than to do it for real. And "the message" is sent to leaders nonetheless.

Another nine days to go to see whether what happened in Quebec and Scotland will happen for the Brexit. We know however that the situation is somewhat different, in particular in the sociodemographic profile of the supporters for the two sides. Support for change in the actual campaign comes more from older people, who tend to turnout in larger proportions.

**Notice on methodology: In the graphs, each point represents a poll estimate positioned at the middle of the fieldwork; lines represent the likely change in support estimated using Loess (Epanechnikov, 0.65).

 For methodologists and other interested people

A question to ask is whether there is more variation according to mode and whether there is variation within mode. The next graph shows a box-and whiskers plot of the variation according to mode in support for Stay with proportional attribution of non-disclosers. The graph again illustrates that support for Stay is estimated higher by telephone polls. However, there is not much difference between modes in the level of variation and not that many polls differ significantly from other polls using the same mode. Two poll estimates by Survation are significantly higher than the other web opt-in polls and one YouGov poll is somewhat lower. For telephone polls, ICM and ORB each have two polls that are somewhat low.

 A similar graph done with estimates using non-proportional attribution of non-disclosers show a similar portrait. However, this procedure reduces variance among telephone polls and now show two Ipsos-Mori and one ComRes polls somewhat higher than the other telephone polls.

A general conclusion from this analysis would be that the major difference between modes is in the estimates -- in this case the median estimate -- not in variation. And there is not much difference within modes either.

jeudi 9 juin 2016

To Brexit or not to Brexit,...

Hi everybody,

Welcome to my first analysis of the polls regarding the Brexit. I will perform the same analysis as for the Scottish referendum, using graphs of local regressions. I will look at the likely change in support for the Brexit and at the differences between modes.

First, here is the graph that takes into account all the polls conducted since January 2016. The dots represent poll estimates. The lines represent the estimation of change using local regressions (epanechnikov .65 for the specialists).

The graph shows that the two sides are now practically at the same level according to the published polls. It also shows that the proportion of non-disclosers -- including the undecideds and those who say they will not vote -- has decreased since March, from around 17% to 11%. It is the Leave side that has gained most from the decrease of the non-disclosers. The proportion of supporters for Stay has remained the same over the period.

However, the graphs also allow to notice the the proportion of non-disclosers -- the dots in the graph -- varies much, from 4% to 30%. This proportion varies by pollster  -- from an average of 4.7% for ORB to 27.8 for TNS.-- and by mode -- 16.8% for the Web polls, 10.2% for the telephone polls. Note that the proportion of non-disclosers  was not published for three ORB polls. Since this would have biased the analyses, I attributed a proportion of 5% of undecideds to these ORB polls and modified the proportion of stay and leave accordingly.

The following graph illustrates the change in support when undecideds are allocated proportionally to each side, which is the usual procedure for all the pollsters. The portrait is quite the same as with the preceding graph, i.e., the two sides are at par, with a possible tiny advantage for stay.

For the Scottish referendum, I had suggested that a non-proportional attribution of non-disclosers be used as was the case for the Quebec 1995 referendum. I had proposed to attribute 67% of the non-disclosers to the No side and 33% to the Yes side. This procedure produced a very good prediction. I had predicted at least a 7 points difference between the two sides. It ended up at 10 percentage points. The argument here is not that the non-disclosers really distribute themselves in these proportions. This procedure is a way to correct for a number of phenomena. It is likely that partisans of the status quo are less likely to be in the samples since generally they are more likely to be older and harder to contact. It is even more likely with Web polls. It is also likely that partisans of the status quo are less prone to answer polls and, when they do, to reveal their vote. In addition, the fact that the proportion of non-disclosers vary between pollsters means that it is a feature of the methods used more than of the real proportion in the population. Using a non-proportional attribution means that the higher the proportion of non-disclosers the higher the proportion that is attributed to the status quo. Empirically, for the polls conducted in 2016, there is a positive correlation between the proportion of non-disclosers and the proportion of supporters for Leave. This tends to justify the non-proportional attribution.

One could argue that the situation is different than for the Scottish referendum since, for instance, the older people were more likely to support the No side in Scotland while it is the opposite for the Brexit. Older people seem more likely to support the Leave side. However, this may be partly due to a paradox where older people who are for Leave are more likely to answer polls.

Since I do not have a theoretical or empirical justification to change the attribution that I used in the Scottish referendum, I decided to use the same. Here is the graph that I get using this procedure. The two sides are now about five points apart, which is -- I think -- more realistic.

In conclusion, it will be very interesting to follow the campaign in the next two weeks. My next post will deal with  the substantial differences in the portraits traced by web polls compared to telephone polls.