Sunday, January 22, 2012

Polls and what to make of them

With the republican primaries going on in the USA and the always present polls for coalition governments in Europe, polls have become part of our daily lives. If polls are made properly, they are good for governments and the general public because they can tell us an indication on how the majority of people thinks about certain subjects. A government can use polls to see the effects of their policy on the population and might decide upon a change in it midterm, because their voters disapprove of it.

However polls are dangerous things, because all to often they are misinterpreted and taken more seriously than they should. One problem of polls is that people might not tell the the truth in a poll, because they are not anonymous. For instance: they might give the social acceptable answer of voting for a social party and then vote for an extreme right one (In Dutch: Links lullen, Rechts stemmen). Also people that are asked during a poll might not actually know what they would vote for and just give a random answer depending on what they have seen on that day on TV. And finally even if somebody truthfully answers he might not go voting because the weather is bad on voting day. And these are just some problems, there are many more...

Next to these inherent problems of polling there are also problems with to low sample sizes (that means that not enough people take part in the poll). To give an example (this involves some statistics 1.02): In the Dutch assembly there are 150 seats. So the question is: how many people do you need to ask before you can say up to 1 seat in uncertainty per party how the people would vote. To calculate the uncertainty you need to use a Poisson distribution and take roughly two times the standard deviation for the uncertainty. This amounts to roughly one over the square root of the number of people asked (it also depends on how much seats you expect, parties with less seats are predicted more accurately). Here we need an accuracy of 1/150, since there are 150 seats. So to get within 1 seat you need 150 square or 22500 voters asked. If you want an accuracy of 2 seats you need 22500/4 voters, if you need 3 seats 22500/9 etc. The average poll in the Netherlands has about a 1000 people in it, giving it an accuracy of 3% of the votes or 4.5 seats in the Dutch parliament. (please correct me if the math I did was wrong)

Now what does all of this math tell us? That any poll that we see in the Dutch news is probably inaccurate to about 4 seats per party. That makes questions like: so your party rose by one seat in today's poll, what do you think about that? Totally ridiculous. The same math also applies to other countries: If the number of people asked in CNN is the same, a lead of 3% in the polls for a US candidate does not really tell you anything.

In conclusion: most daily polls do not really tell much except for when they show major differences. What those polls can tell us is a trend: a political party which is falling by numerous polls over a long time(e.g. Dutch CDA) still needs to be worried and will probably need to adjust its policies. This is because with consequetive polls the uncertainty shrinks, simply because more people were asked. A political party which is bouncing up and down a bit in the polls should not worry, that is just statistical noise.

A final note: this post deals with acceptable polls with good techniques. I do not classify the polls from Maurice de Hond (most cited poll in the Netherlands) in here. As far as i am concerned his polls are of very little value to predict outcomes of elections.

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