In my previous post – all of two days ago – I noted that Nanos was consistently publishing estimates for Liberal support that were much higher than the other polling firms: more than what could plausibly attributed to sampling error.

But that was two days ago. Since then, Nanos has joined the crowd (click on the graph for a full-sized version):

What’s going on?

This is cross-posted at my blog Worthwhile Canadian Initiative.

There are a lot of published opinion polls out there: I count 41 since September 8. The trouble is that many of them contradict each other – just what are we supposed to make from all this? Let’s haul out our introductory statistics textbooks and take a closer look.

Firstly, let’s get an idea of the sort of variations that we should expect to see, that is, the inherent uncertainty with drawing random samples. Ekos, Nanos and Harris-Decima are all publishing daily tracking polls, with announced 95% confidence intervals of 1.6%, 3.1% and 2.6%, respectively. If sampling error were the only source of uncertainty, what would a typical deviation between Nanos and Harris-Decima look like? (I’m choosing those two because they have the larger announced MOE; what follows will be an upper bound for the variations we should expect.) The answer is not 3.1 + 2.6 = 5.7%.

If we play around a bit with the arithmetic of confidence intervals, the standard deviations for the Nanos and Harris-Decima estimates are 1.58 and 1.33, respectively. If Nanos and Harris-Decima are operating independently, the standard deviation for the difference between the two estimates is (1.58² + 1.33²)^1/2 = 2.06. From this, the half-width of the 95% confidence interval is 1.96*2.06 = 4.05.

If sampling error were the only thing to worry about, the chances of seeing a gap of more than four percentage points is 1 in 20. It also follows that the probability of observing a discrepancy of 5 or more points is 1 in 65, and the odds of seeing a 6-point gap are 274:1 against.

So much for the theory; what are the variations we’re actually seeing? First up is the support for the Conservative party; click the image for a full-sized version. In all the graphs that follow, the scale of the vertical axes is the same, so that differences in poll results are the same distance apart.

So far, so good: it is almost always the case that the polling firms differ by 3 percentage points or fewer. Indeed, there have been many days where two or three polling firms come up with the same estimate. It’s also interesting to note that of the 26 polls published since September 15, only two are outside the range of 35-38%.

Now the New Democrats; again, click the image for a larger version.

The range of variation is greater than was the case for that of the Conservatives, but at least some of that can be attributed to the fact that NDP support appears to have been growing during this period. Aside from Ekos – which started with high initial support – all the polling firms show a discernible trend upwards.

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From an article in Wednesday’s Le Soleil:

Rimouski-Neigette-Témiscouata-Les Basques : la famille souverainiste divisée: L’ex-députée bloquiste Louise Thibault, élue en 2004 et réélue en 2006, souhaite un nouveau mandat comme «souverainiste indépendante», alors que le Bloc québécois y présente Claude Guimond, l’ex-président de l’Union des producteurs agricoles du Bas-Saint-Laurent, choisi au terme d’une assemblée d’investiture contestée.

Not only will the sitting BQ MP be running as an independent, the Bloc’s riding association was deeply divided in its choice of candidate:

En octobre 2007, quelque 400 militants du Bloc ont choisi Claude Guimond, qui n’aurait devancé son adversaire Christian Gionest que d’une trentaine de voix. M. Guimond jouit de l’appui de l’ex-députée Suzanne Tremblay. Une clientèle fragmentée sur le thème de la souveraineté mais aussi à gauche puisque le néo-démocrate Guy Caron, qui avait récolté un très respectable 10 % des votes au scrutin de 2006, est de nouveau sur les rangs.

This may be closer than what previous patterns would suggest.

For people living outside the Quebec City area, the Conservative breakthrough here might have been the biggest surprise of the 2006 election. But it shouldn’t have been. This region has never been a sovereignist stronghold, nor is it one of leftist activism.

This time around, the trend is for an even weaker Liberal showing – if that’s even mathematically possible – and the Bloc Québécois (like the PQ) is still trying to figure out a way to re-connect with this region. So even though the Conservatives won a couple of these ridings by very slim margins in 2006, it’s hard to see how they could lose them in 2008:

Beauport-Limoilou: In 2006, Conservative Sylvie Bouchard managed to defeat a well-known sitting BQ MP. There’s little reason to believe that she can’t hold it.

Charlesbourg-Haute-Saint-Charles: Pretty much the same story as above. Daniel Petit should hold for the Conservatives

Louis-Hébert: A squeaker last time around, but if Luc Harvey could beat the highly-respected Roger Clavet in 2006, he should be able to defend the seat against a BQ newcomer.

Louis-St-Laurent: My home riding. Josée Verner won this with 58% of the vote last time; if there is a safe Conservative seat in Quebec, this is it.

Portneuf-Jacques-Cartier: Noted radio host André Arthur won in 2006, and since then he has voted with the Conservatives whenever they have needed his vote. The Conservatives have decided not to run a candidate against Arthur this time, for two reasons. Firstly, there’s the risk that the BQ would benefit from vote-splitting between Artur and the Conservatives. Secondly, the current situation suits everyone concerned: the Conservatives have a vote when they need it, and they don’t have to worry about getting Arthur – whose picture accompanies dictionary definitions of “loose cannon” – to maintain caucus discipline. Arthur should win again handily.

Québec: This is the question mark. The BQ’s Christiane Gagnon won with 42% of the vote of this downtown riding in 2006. Since then, a couple of things have happened. Firstly, there’s the consolidation of the Conservative position in the region. Secondly, there was the ADQ sweep in the 2007 provincial election. Agnès Maltais was able to hold onto the provincial riding of Taschereau for the PQ in 2007, and to the extent that Taschereau and the federal riding of Québec overlap, that suggests that Gagnon has a decent chance of holding out as well. But Québec also overlaps with the provincial ridings of Jean-Lesage and Vanier, both of which went ADQ. Moreover, the Liberals – who won 30% of the vote in 2006 – have botched their nomination process; some federalist voters who were in the habit of voting Liberal may decide to vote Conservative this time. Finally, there’s also the possibility that some progressive BQ voters might drift off to the NDP or the Greens. Christiane Gagnon may hold this seat, but it will be a very close-run thing.

Across the river, Maxime Bernier will easily hold Beauce, despite his demotion from cabinet. The ridings of Lévis-Bellechasse and Lotbinière-Chutes-de-la-Chaudière are in the hardest-of-hard-core ADQ territory; it’s difficult to imagine anyone taking these ridings away from sitting Conservative MPs.