Page 329 - Statistics for Dummies

Chapter 19: Two-Way Tables and Independence
thought; in the details of the report you see the study was conducted on a
total of 20 men who were all in excellent health, on low-fat diets, who exercised
several times a week. Ten men in good health ate two eggs a day and their cho-
lesterol didn’t change much, compared to ten men who didn’t eat two eggs per
day. Do these results carry over to the entire population? Can’t tell — the sub-
jects in the study don’t represent the rest of us. (See Chapter 17 for the scoop
on evaluating experiments.)
In this section, you see how to put the results from a two-way table into
proper perspective in terms of what you can and can’t say and why. This
basic understanding gives you the ability to critically evaluate and make deci-
sions about results presented to you (not all of which are correct).
Checking for legitimate cause and effect
Researchers studying two variables often look for links that indicate a cause-
and-effect relationship. A cause-and-effect relationship between two categorical 313
variables means as you change the value of one variable and all else remains
the same, it causes a change in the second variable — for example, if being on
an aspirin regimen decreases the chance of developing subsequent polyps in
colon-cancer patients.
However, just because two variables are found to be related (dependent)
doesn’t mean they have a cause-and-effect relationship. For example, observ-
ing that people who live near power lines are more likely to visit the hospi-
tal in a year’s time due to illness doesn’t necessarily mean the power lines
caused the illnesses.
The most effective way to conclude a cause-and-effect relationship is by con-
ducting a well-designed experiment (where possible). All the details are laid
out in Chapter 17, but I touch on the main points here. A well-designed experi-
ment meets the following three criteria:
✓ It minimizes bias (systematic favoritism of subjects or outcomes).
✓ It repeats the experiment on enough subjects so the results are reliable
and repeatable by another researcher.
✓ It controls for other variables that may affect the outcome that weren’t
included in the study.
In the earlier section “Describing a dependent relationship,” I discuss a study
involving the use of aspirin to prevent polyps in cancer patients. Because of
the way the data was collected for this study, you can be confident about the
conclusions drawn by the researchers; this study was a well-designed experi-
ment, according to the criteria established in Chapter 17. To avoid problems,
the researchers in this study did the following:

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