SCI199Y: October 8, 1996

Required for next week

• Nothing!!!
• We will meet in Robarts Library, 4th floor, Room 4055 (a room full of PCs).

Some technicalities on polls

The margin of error

In many newspaper articles on polls, the result of the poll will be accompanied by a statement something like "polls of this size are accurate to within 3 percentage points, 19 times out of 20". None of the polls at Politics Now on the internet seem to include this, but they do provide information on the number of people polled for each poll, which is usually good enough.

The margin of error is computed using the assumption that people in the population are one of two types: i.e., they will either vote for Clinton or Dole, they will either vote Yes or No on the referendum, they are either pro-choice or pro-life, and so on. Let's call the two types Red and Green. The margin of error is computed as

In fact, we don't know the fraction Red, (that's why we're conducting the poll), so this is usually replaced by one-half. So now the margin of error is a simple function of the size of the sample:

Here is a little table:

Three (or more) candidates

The formula given above doesn't work for more than three candidates, and although it's possible to compute a margin of error for such polls, it's a bit trickier. Since Perot is a really distant third, the more complicated formula would not change the Clinton-Dole comparison by more than a tenth of a percentage point or so.

Problems with polls

Of course, people aren't really red and green balls, and their opinions can change due to a variety of factors. Pollers try to poll 'likely voters', rather than 'registered voters', but how they determine this is not always clear. In the Quebec referendum last year, a significant number (10-15%) of the respondents to the polls said they were 'undecided'. When the 'yes' tally was prepared for the headline articles, these undecided voters were allocated to either Yes or No, according to a complicated formula based on their answers to other questions. Typically that meant that undecideds were split about 70-30 for No.

Often the results of many polls are plotted in a time series, so people can play 'spot-the-trend'. However, the margin of error applies to each poll separately, and not to the whole sequence of polls. The luck of the draw would be expected to lead to a few 'rogue' polls. What is perhaps more worrisome, from a social policy perspective, is that the polls themselves might influence the outcome of later polls, and in fact the election.

In the Globe & Mail this week

• ``Guess what? You're richer (on average)''. B. Little, Oct 7, A6. A Middle Kingdom article summarizing a recent report from Statscan on three economic measures: total assets, net worth, and household debt. Net worth has been increasing, largely due to investment income in employees' pension plans and retirement savings plans. Nice graphic.
• ``Vaccine could halt spread of MS''. W. Immen, Oct. 1, A6. A study in Oregon was published in Nature Medicine describing a vaccine that was tested on advanced MS patients. Seventeen patients were given the vaccine, and six others a placebo. Six of the seventeen patients remained stable for a year, while the disease progressed in 11 others, and in the six on placebo.
• ``Quebeckers want votes delayed''. R. Mackie, Oct. 4, A1& A8. Describes the September poll on the referendum question taken by Léger and Léger (it's even), and gives a polltrack for the past 18 months. Apparently Léger and Léger poll every month.
• ``Cod coming back, fishermen say''. K. Cox, Oct. 5, A1. Subheadline is ``Minister under pressure to end moratoriums in waters off Newfoundland.''
• ``Investors hope for medical breakthroughs''. M. Stinson, Oct. 7, B1. Discussion of the new biotechnology companies, and their prospects for investment.

Monty Hall again... This rather elegant solution was posted on the internet. I think it's okay...

There are two strategies:

1. You stay with your initial pick all the time.
2. You switch doors every time.

In case 1, the probability of winning is 1/3. In case 2, the probability of losing is 1/3, because you will lose only if you had picked the winning door first.

Technical note: theory behind the margin of error

• We assume there is a proportion of the total population that is Red (e.g. will vote Clinton): this is called the true proportion.
• The proportion of the sample that will vote no is assumed to estimate the true proportion. This estimate has some sampling error.
• If the error in the poll is only due to sampling (this is a big if), then this error can itself be estimated. Denote the true proportion by p, and the sample size by n.
• The theory behind the binomial distribution shows that the error in the estimate is given by . We don't know p, but use the sample estimate again (or just use which gives the largest possible margin of error for 0<p<1.)
• The interval given by

  

  catches the true proportion 95% of the time (19 times out of 20). The factor 2, the 95% and the comes from the 'bell curve', or normal distribution, used here as an approximation to the binomial distribution.

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