Book T of C

Chap T of C

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This is the 2007 version. Click here for the 2017 chapter 01 table of contents.

The letter "N" is used to indicate the number of subjects contributing data to an experiment or opinion poll. N=500 means 500 subjects were used, or 500 people were polled. This number has a powerful influence on the reliability of the results.

What is the possible effect of taking a small sample?

If you take a small sample, even a small *random* sample, you can get very unusual and misleading results. For example, if you drew the names of three students at random from a college registration list, you might come up with three students who were over six feet tall, purely by coincidence. But if you used a random sample of 100 students, the average height of students in the sample would resemble almost exactly the average height of the entire student body.

Why is it possible to say, with confidence, that a sample of 100 will have an average height within an inch or two of the entire student body? It is because of the so-called "Law of Large Numbers." The larger the N, the more closely a random sample will approximate its parent population. This law is really an outgrowth of basic laws of probability. Random variations go every which way. The larger the N, the more likely it is that all the variations will cancel each other out and leave you with an accurate average value.

Students sometimes ask how large an N is required before the results of a poll become trustworthy. The answer depends on the level of precision desired and the amount of variation in the characteristic being measured. A national opinion poll using a random sample of a 500 people should produce results that are very accurate, providing the sample is truly unbiased. A smaller sample of 25 or so may give representative results if there is not a great deal of underlying variation. Polls based on 5 or 10 people are seldom reliable for anything except expressing the opinions of 5 or 10 people.

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