What's the difference between a poll and a ballot?

Michael Thompson

If the differing results of PJ Online’s recent poll on the planned changes to the Royal Pharmaceutical Society’s charter and the Society’s own ballot on the matter are to be believed — and why shouldn’t they — then the answer must be “quite a lot”.

In our poll, admittedly small, 68 per cent of participating voters (134 out of a possible 8,834) were against the change. But the Society’s ballot, rather larger but still only achieving a 22 per cent turnout, managed to get 78 per cent in favour (10,698 votes cast out of a possible 48,115). There are two possible explanations for such a difference, but one must be discounted since it is just not credible to suggest that a vote conducted by the Electoral Reform Society is open to tampering. The only credible explanation is that the participants in the two votes represented different constituencies.

It has been suggested to me that the reason could be that PJ Online attracts the mavericks and the disenchanted. I prefer to think that this is not the case, although some might be proud to bear that label. But this still leaves me wondering exactly why the difference was so wide and whether it actually matters.

The answer to the latter question is “probably not”. Why? Well our poll is just a finger in the air. It shows that there is a group of people who feel strongly enough about something to want to make themselves heard publicly.

And the answer to the first? Probably that just as in any other vote, it’s the activists who make the noise, but the wider electorate that makes the decision.

So back to my original question — and just for fun — can anyone use ststistics to show that the two results are the same, after all the dictionary says that a ballot and a poll are the same. I'd like to know whether the difference in the two results is statistically significant or could be down to chance. It took me three attempts to pass my stats exam at the Square nearly 30 years ago, so I’m hardly competent. If someone wants to take on the challenge, here it is. First, show that the difference is real using one statistical method; then prove that it is not using another.

And show your workings!