"But the poll, as emphasized by La Presse, showed the Liberal Party climbing to 19 per cent of decided voter support, up significantly from the meagre 14.2 per cent share of votes it received in the province last May" declares The Hill Times.
"The Liberals, on the other hand, have gained nine points in Quebec since that same June poll, and sit at 19 per cent. Support for the Bloc Québécois is stagnating at only 22 per cent" states Maclean's confidently.
In the poll quoted by the Hill Times and Maclean's they conveniently ignore the fact that according to the poll, the Conservatives are now sitting at 25% in Quebec (compared to their 16.5% result in the 2011 election). A far greater increase than the Liberals who only increased from 14.2% (2011 election) to 19%. Neither publication even mentioned the Conservatives' numbers, I had to go to the original article in La Presse to get that. So I'm suspicious that these articles are biased already.
In the poll quoted by the Globe and Mail, the Liberals have gained 3% so they now sit at 22%. The Conservatives hover around 37% and the NDP around 28%. Can we say that the increase in Liberal support is significant? For the case where a party or person has increased their support by 20% in a single week, I think no one will argue that the increase is not significant. Conversely, if a party or person only increased in support by 1%, I think very few people would argue that the increase is significant. But where do we draw the line and how?
The poll says it has an accuracy of plus or minus 3%, 19 times out of 20. So an increase in 3% is pushing that limit, right? But what if the last poll slightly underestimated the actual Liberal support by 1.5% and this poll slightly overestimates the actual Liberal support by 1.5%? In which case the actual difference would be almost zero but the reported difference would still be 3%.
In scientific terms, if we are trying to determine if a change is significant there are a number of tools and methods available and some are far more thorough than others. I'd like to show a very simple way.
1. Take the difference between the two values in question. In our case, the difference in the Liberal support was +3%.
2. Assuming that the errors are independent and Gaussian, add the standard errors of the two polls in quadrature (add the squares and take the square root of the total). In our case the square root of 9 + 9 is about 4.2
We would then say that the difference in Liberal support is 3% plus or minus 4%, 19 times out of 20.
So is it possible that the Liberal "surge" could simply be the result of random errors in the poll? Absolutely.
Is it more likely that the Liberals are increasing in support than they are decreasing? Of course.
Would I feel confident stating that they are and drawing a number of conclusions about the direction of the party? No.