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Part V: Statistical Studies and the Hunt for a Meaningful Relationship
✓ If the data show a downhill pattern as you move from left to right, this
indicates a negative relationship between X and Y. As the X-values increase
(move right) the Y-values decrease (move down) by a certain amount.
✓ If the data don’t seem to resemble any kind of pattern (even a vague
one), then no relationship exists between X and Y.
One pattern of special interest is a linear pattern, where the data has a gen-
eral look of a line going uphill or downhill. Looking at Figure 18-1, you can see
that a positive linear relationship does appear between number of cricket
chirps and the temperature. That is, as the cricket chirps increase, the tem-
perature increases as well.
In this chapter I explore linear relationships only. A linear relationship between
X and Y exists when the pattern of X- and Y-values resembles a line, either
uphill (with a positive slope) or downhill (with a negative slope). Other types
of trends may exist in addition to the uphill/downhill linear trends (for exam-
ple, curves or exponential functions); however, these trends are beyond the
scope of this book. The good news is that many relationships do fall under the
uphill/downhill linear scenario.
Scatterplots show possible associations or relationships between two vari-
ables. However, just because your graph or chart shows something is going
on, it doesn’t mean that a cause-and-effect relationship exists.
For example, a doctor observes that people who take vitamin C each day
seem to have fewer colds. Does this mean vitamin C prevents colds? Not
necessarily. It could be that people who are more health conscious take
vitamin C each day, but they also eat healthier, are not overweight, exercise
every day, and wash their hands more often. If this doctor really wants to
know if it’s the vitamin C that’s doing it, she needs a well-designed experi-
ment that rules out these other factors. (See the later section “Explaining the
Relationship: Correlation versus Cause and Effect” for more information.)
Quantifying Linear Relationships
Using the Correlation
After the bivariate data have been organized graphically with a scatterplot
(see the preceding section), and you see some type of linear pattern, the
next step is to do some statistics that can quantify or measure the extent
and nature of the relationship. In the following sections, I discuss correla-
tion, a statistic measuring the strength and direction of a linear relationship
between two variables; in particular, how to calculate and interpret correla-
tion and understand its most important properties.

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