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Part V: Statistical Studies and the Hunt for a Meaningful Relationship
✓ Randomly chose who took the aspirin and who received a fake pill
✓ Had large enough sample sizes to obtain accurate information
✓ Controlled for other variables by conducting the experiment on patients
in similar situations with similar backgrounds
Because their experiment was well-designed, the researchers concluded
that a cause-and-effect relationship was found for the patients in this study.
The next test is to see whether they can project these results to the popula-
tion of all colon-cancer patients. If so, they are truly entitled to the headline
“Aspirin Prevents Polyps in Colon-Cancer Patients.” The next section walks
you through the test.
Whether two related variables are found to be causally associated depends on

how the study was conducted. A well-designed experiment is the most con-
vincing way to establish cause and effect. In cases where an experiment would
be unethical (for example, proving that smoking causes lung cancer by forcing
people to smoke), a mountain of convincing observational studies (where you
collect data on people who smoke and people who don’t) would be needed to
show that an association between two variables crosses over into a cause-and-
effect relationship.
Projecting from sample to population
In the aspirin/polyps experiment discussed in the earlier section “Describing
a dependent relationship,” I compare the percentage of patients developing
subsequent polyps for the aspirin group versus the non-aspirin group and
got the results 17% and 27%, respectively. For this sample, the difference is
quite large, so I’m cautiously optimistic that these results would carry over
to the population of all cancer patients. But what if the numbers were closer,
such as 17% and 20%? Or 17% compared to 19%? How different do the pro-
portions have to be in order to signal a meaningful association between the
two variables?
Percentages compared using data from your sample reflect relationships
within your sample. However, you know that results change from sample to
sample. To project these conclusions to the population of all colon-cancer
patients (or any population being studied), the difference in percentages
found by the sample has to be statistically significant. Statistical significance
means even though you know results will vary, even taking that variation into
account it’s very unlikely the differences were due to chance. That way, the
same conclusion about a relationship can be made about the whole popula-
tion, not just for a particular data set.

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