[T4.1] Statistical reasoning

Samples

Perhaps the most important uses of statistical reasoning are in dealing with samples. For example, a pollster who wants to find out how many people in Hong Kong are satisfied with the performance of the Chief Executive doesn't interview everyone in Hong Kong, for obvious reasons. Instead, the pollster interviews a sample of Hong Kong residents, and uses statistical techniques to draw conclusions about the population as a whole.

But sampling isn't limited to surveys and opinion polls. In manufacturing industries, sampling is used in quality control; for example, from the number of defects in a sample of electrical components, one can infer the overall reliability of the manufacturing process. In medical research, sampling is used to identify health risks; for example, from the difference in heart disease rates between a sample of smokers and a sample of non-smokers, one can infer the overall effect of smoking on the risk of developing heart disease. In general, sampling is necessary in any case where examining every member of the relevant population of people or things would be too expensive or too time consuming.

In the next few sections, we are going to look at reasoning from samples, and some common ways it can go wrong. Ideally, what one wants from a sample is that the properties you are interested in are the same in the sample as in the whole population. For example, the pollster hopes that the proportion of people who are satisfied with the Chief Executive's performance is the same in the sample as in the population of Hong Kong as a whole. In general, this kind of assumption can fail in two different ways--bias and sampling error. We will examine them in turn.

The next few sections cite several statistical results without proof. If you want to see where they come from, see any statistics text (e.g. Larry Gonick and Woollcott Smith (1993), The Cartoon Guide to Statistics. New York: HarperCollins).