Page 271 - Statistics for Dummies

Chapter 16: Polls, Polls, and More Polls
A good sample is selected randomly
A random sample is one in which every possible sample (of the same size) has
an equal chance of being selected from the target population. The easiest exam-
ple to visualize here is that of a hat (or bucket) containing individual slips of
paper, each with the name of a person written on it; if the slips are thoroughly
mixed before each slip of paper is drawn out, the result will be a random sample
of the target population (in this case, the population of people whose names are
in the hat). A random sample eliminates bias in the sampling process. 255
Reputable polling organizations, such as the Gallup Organization, use a
random digit-dialing procedure to telephone the members of their sample. Of
course, this excludes people without telephones, but because most American
households today have at least one telephone, the bias involved in excluding
people without telephones is relatively small.
Beware of surveys that have a large but not randomly selected sample.
Internet surveys are the biggest culprit. Someone can say that 50,000 people
logged on to a Web site to answer a survey, and that means the person post-
ing this site has gotten a lot of data. But the information is biased; research
shows that people who respond to surveys tend to have stronger opinions
than those that don’t respond. And if they didn’t even select the participants
randomly to start with, imagine how strong (and biased) the respondents’
opinions would be. If the survey designer sampled fewer people but did so
randomly, the survey results would be more accurate.
A good sample is large enough for the results to be accurate
If you have a large sample size, and if the sample is representative of the
target population and is selected at random, you can count on that informa-
tion being pretty accurate. How accurate depends on the sample size, but the
bigger the sample size, the more accurate the information will be (as long as
that information is good information). The accuracy of most survey questions
is measured in terms of a percentage. This percentage is called the margin of
error, and it represents how much the researcher expects the results to vary if
she were to repeat the survey many times using different samples of the same
size. Read more about this in Chapter 12.

A quick and dirty formula to estimate the minimum amount of accuracy of a
survey involving categorical data (such as gender or political affiliation) is to
take 1 divided by the square root of the sample size. For example, a survey of
1,000 (randomly selected) people is accurate to within ±0.032, or 3.2 percent-
age points. (See Chapter 12 for the exact formula for calculating the accuracy
of a survey.) In cases where not everyone responded, you should replace
the sample size with the number of respondents (see the “Following up, fol-
lowing up, and following up” section later in this chapter). Remember, these
quick-and-dirty estimates of accuracy are conservative; using the precise
formulas gives you accuracy rates that are often much better than these.
(See Chapter 13 for details.)

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