SCI199Y: October 10, 1995

Required for two weeks from now

• Project 1

Some technicalities on polls

Allocating the undecideds

In the poll reported on September 30 in the Globe and Mail (front page), the results were given as 53.2% for no, and 46.8% for yes. Later in the article, the results were given as:

According to the reporter, the undecideds and won't says are grouped, and their votes are allocated in the ratio 70% to no, 30% to yes. (In fact my calculation shows that 76% was assigned to no.)

Later in the same article, a study from three weeks earlier is quoted as giving the results 49.8% for no and 50.2% for yes. The detailed breakdown was:

In this poll about 50% of the undecideds and won't says were were allocated to the no group. So a large part of the shift is due to a change in the method of allocation.

The margin of error

For the poll quoted above (the first one), it is also stated in the article that 1,006 people were polled, and that the poll has a margin of error of 3.1%, 19 times out of 20. The way to compute the margin of error is simple:

In this poll, that is

. The theory behind this is sketched on the next page.

The polling trend

In an article on September 26 in the Globe and Mail, headlined "Polls show trend", the following results were given:

(I've added the poll reported on Sept. 30 myself.) Does it look like a trend to you?

In the news this week...

• "Prostate cancer epidemic looms": G &, Sept. 27 (A10) Summarizes an article in the latest issue of the Canadian Journal of Public Health.
• "Canadian banks the most robbed": G & M, Sept. 28 (A2) But the take per robbery is the lowest... [with accompanying table]
• "High school graduates caught in job vacuum": G & M, Oct.3 [with accompanying graphic]
• "Eating disorders on the increase": G & M, Oct. 5 (A14) New studies suggest that both anorexia and bulimia occur up to twice as frequently as reported in earlier studies.

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.

Theory behind the margin of error

• We assume there is a proportion of the total voting population that will vote no (often 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

  

  , and the sample size by

  

  .

• The theory behind the binomial distribution shows that the error in the estimate is given by

  

  . We don't know

  

  , but use the sample estimate again.

• 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.

About this document ...

This document was generated using the LaTeX2HTML translator Version 0.6.4 (Tues Aug 30 1994) Copyright © 1993, 1994, Nikos Drakos, Computer Based Learning Unit, University of Leeds.

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