Page 64 - Statistics for Dummies

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Part I: Vital Statistics about Statistics
In each of these examples, a question is posed. And in each case, you can
identify a specific group of individuals being studied: the American people,
all planted crops in Wisconsin, all breast cancer patients, and all cereal boxes
that are being filled, respectively. The group of individuals you want to study
in order to answer your research question is called a population. Populations,
however, can be hard to define. In a good study, researchers define the popu-
lation very clearly, whereas in a bad study, the population is poorly defined.
The question of whether babies sleep better with music is a good example of
how difficult defining the population can be. Exactly how would you define
a baby? Under three months old? Under a year? And do you want to study
babies only in the United States, or all babies worldwide? The results may be
different for older and younger babies, for American versus European versus
African babies, and so on.
Many times researchers want to study and make conclusions about a broad
population, but in the end — to save time, money, or just because they don’t
know any better — they study only a narrowly defined population. That short-
cut can lead to big trouble when conclusions are drawn. For example, suppose
a college professor wants to study how TV ads persuade consumers to buy
products. Her study is based on a group of her own students who partici-
pated to get five points extra credit. This test group may be convenient, but
her results can’t be generalized to any population beyond her own students,
because no other population was represented in her study.
Sample, random, or otherwise
When you sample some soup, what do you do? You stir the pot, reach in with
a spoon, take out a little bit of the soup, and taste it. Then you draw a conclu-
sion about the whole pot of soup, without actually having tasted all of it. If
your sample is taken in a fair way (for example, you didn’t just grab all the
good stuff) you will get a good idea how the soup tastes without having to eat
it all. Taking a sample works the same way in statistics. Researchers want to
find out something about a population, but they don’t have time or money
to study every single individual in the population. So they select a subset of
individuals from the population, study those individuals, and use that infor-
mation to draw conclusions about the whole population. This subset of the
population is called a sample.
Although the idea of a selecting a sample seems straightforward, it’s anything
but. The way a sample is selected from the population can mean the difference
between results that are correct and fair and results that are garbage. Example:
Suppose you want a sample of teenagers’ opinions on whether they’re spend-
ing too much time on the Internet. If you send out a survey using text messag-
ing, your results won’t represent the opinions of all teenagers, which is your
intended population. They will represent only those teenagers who have access
to text messages. Does this sort of statistical mismatch happen often? You bet.

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