I would normally take care in posting something about “the curve” in law circles, as there is a good chance that somebody who graduated law school will break out in hives. Those who do break out in hives might be heartened to know that the curve has utility far beyond determining law school mark, one such is use is in explaining how polling works. With the results of most recent election in B.C. and the recent spotty track record of polls in various Canadian elections, I have found these recent tribulations fascinating as I distinctly remember a few years ago public conjecture on the possibility of banning polls close to elections because the results of the polls were skewing the actual elections by influencing people’s voting decisions. So where does the curve come in? Well first a basic description of the the curve.
If the centre of the curve is the mean or average, each section away from the centre is a standard deviation, so 68.2% of all results will be within one standard deviation (in either direction) of the average and 95.4% of the results will be within two standard deviations from the mean. Calculating square roots of numbers comes in here and I’m going to skip that part. I am an amateur at this and in doing research on this I discovered a post by an expert which goes into greater detail with greater understanding than I, and as I tell law students, “don’t recreate the wheel, if the experts have done something, see what they had to say”, so if you want to read more about this I recommend going to Jeffrey Rosenthal’s “Margins of Error in Opinion Polls”. For the purposes of polling just remember that the standard deviation is the measure of the distance or range between possible answers and the margin of error (plus or minus X% points 19 times out of 20) is calculated using the standard deviation represented using the curve. Polls seek to reach a 95% confidence level which is two standard deviations away (in either direction) from the mean or centre of the curve. Polls are not actually designed to predict an outcome, the 19 out of 20 simply means that 19 times the results will fall within two standard deviations of the mean. The number of people contacted in a poll affects the margin of error, or the distance between standard deviations or the shape of the curve. Most polls usually do not go beyond 1000, and many contact fewer than that, so that there is a danger that if the group of people contacted is not diverse then the poll results will be skewed.
Getting back to the tribulations of the pollsters in recent years, one wonders why this is occurring, there are a host of possible reasons, but one I wonder about is the possibity that pollsters are only contacting people who retain their land lines for phones, as more and more people abandon their land lines in favour of their mobile is it possible that those who retain land lines fall into a specific segment of society whose similarities are such that they would skew the results of a poll?