Page 79 - Statistics for Dummies

Chapter 4: Tools of the Trade
Correlation versus causation
Of all of the misunderstood statistical issues, the one that’s perhaps the most
problematic is the misuse of the concepts of correlation and causation.
Correlation, as a statistical term, is the extent to which two numerical vari-
ables have a linear relationship (that is, a relationship that increases or
decreases at a constant rate). Following are three examples of correlated
variables:
✓ The number of times a cricket chirps per second is strongly related
to temperature; when it’s cold outside, they chirp less frequently, and
as the temperature warms up, they chirp at a steadily increasing rate. In
statistical terms, you say number of cricket chirps and temperature have
a strong positive correlation.
✓ The number of crimes (per capita) has often been found to be related to
the number of police officers in a given area. When more police officers 63
patrol the area, crime tends to be lower, and when fewer police officers
are present in the same area, crime tends to be higher. In statistical
terms we say the number of police officers and the number of crimes
have a strong negative correlation.
✓ The consumption of ice cream (pints per person) and the number of
murders in New York are positively correlated. That is, as the amount of
ice cream sold per person increases, the number of murders increases.
Strange but true!
But correlation as a statistic isn’t able to explain why or how the relationship
between two variables, x and y, exists; only that it does exist.
Causation goes a step further than correlation, stating that a change in the
value of the x variable will cause a change in the value of the y variable. Too
many times in research, in the media, or in the public consumption of statis-
tical results, that leap is made when it shouldn’t be. For instance, you can’t
claim that consumption of ice cream causes an increase in murder rates just
because they are correlated. In fact, the study showed that temperature was
positively correlated with both ice cream sales and murders. (For more on
correlation and causation, see Chapter 18.) When can you make the causa-
tion leap? The most compelling case is when a well-designed experiment is
conducted that rules out other factors that could be related to the outcomes
(see Chapter 17 for information on experiments showing cause-and-effect).
You may find yourself wanting to jump to a cause-and-effect relationship when
a correlation is found; researchers, the media, and the general public do it all
the time. However, before making any conclusions, look at how the data were
collected and/or wait to see if other researchers are able to replicate the results
(the first thing they try to do after someone else’s “groundbreaking result” hits
the airwaves).

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