Page 37 - Statistics for Dummies

Chapter 1: Statistics in a Nutshell
Drawing Credible Conclusions
To perform statistical analyses, researchers use statistical software that
depends on formulas. But formulas don’t know whether they are being used
properly, and they don’t warn you when your results are incorrect. At the end
of the day, computers can’t tell you what the results mean; you have to figure
it out. Throughout this book you see what kinds of conclusions you can and
can’t make after the analysis has been done. The following sections provide an
introduction to drawing appropriate conclusions.
Reeling in overstated results
Some of the most common mistakes made in conclusions are overstating the
results or generalizing the results to a larger group than was actually repre-
sented by the study. For example, a professor wants to know which Super 21
Bowl commercials viewers liked best. She gathers 100 students from her
class on Super Bowl Sunday and asks them to rate each commercial as it is
shown. A top-five list is formed, and she concludes that all Super Bowl view-
ers liked those five commercials the best. But she really only knows which
ones her students liked best — she didn’t study any other groups, so she can’t
draw conclusions about all viewers.
Questioning claims of cause and effect
One situation in which conclusions cross the line is when researchers find
that two variables are related (through an analysis such as regression; see
the earlier section “Correlation, regression, and two-way tables” for more
info) and then automatically leap to the conclusion that those two variables
have a cause-and-effect relationship.
For example, suppose a researcher conducted a health survey and found
that people who took vitamin C every day reported having fewer colds than
people who didn’t take vitamin C every day. Upon finding these results, she
wrote a paper and gave a press release saying vitamin C prevents colds,
using this data as evidence.
Now, while it may be true that vitamin C does prevent colds, this research-
er’s study can’t claim that. Her study was observational, which means she
didn’t control for any other factors that could be related to both vitamin C
and colds. For example, people who take vitamin C every day may be more
health conscious overall, washing their hands more often, exercising more,
and eating better foods; all these behaviors may be helpful in reducing colds.

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