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Part VI: The Part of Tens
Small sample sizes make results less accurate (unless your population was
small to begin with). Many headlines aren’t exactly what they appear to be
when the details reveal a study that was based on a small sample. Perhaps
even worse, many studies don’t even report the sample size at all, which
should lead you to be skeptical of the results. (For example, an old chewing
gum ad said, “Four out of five dentists surveyed recommend [this gum] for
their patients who chew gum.” What if they really did ask only five dentists?)
Don’t think about this too much, but according to statisticians (who are picky
about precision), 4 out of 5 is much different than 4,000 out of 5,000, even
though both fractions equal 80 percent. The latter represents a much more
precise (repeatable) result because it’s based on a much higher sample size.
(Assuming it’s good data, of course.) If you ever wondered how math and sta-
tistics are different, here’s your answer! (Chapter 12 has more on precision.)
However, more data isn’t always better data — it depends on how well the
data were collected (see Chapter 16). Suppose you want to gather the opin-
ions of city residents on a city council proposal. A small random sample with
well-collected data (such as a mail survey of a small number of homes chosen
at random from a city map) is much better than a large non-random sample
with poorly collected data (for example, posting a Web survey on the city
manager’s Web site and asking for people to respond).
Always look for the sample size before making decisions about statistical
information. The smaller the sample size, the less precise the information. If
the sample size is missing from the article, get a copy of the full report of the
study, contact the researcher, or contact the journalist who wrote the article.
Detect Misinterpreted Correlations
Everyone wants to look for connections between variables; for example, what
age group is more likely to vote Democrat? If I take even more vitamin C,
am I even less likely to get a cold? How does staring at the computer all day
affect my eyesight? When you think of connections or associations between
variables, you probably think of correlation. Yes, correlation is one of the
most commonly used statistics — but it’s also one of the most misunder-
stood and misused, especially throughout the media.
Some important points about correlation are as follows (see Chapter 18 for
all the additional information):
✓ The statistical definition of correlation (denoted by r) is the mea-
sure of strength and direction of the linear relationship between
two numerical variables. A correlation tells you whether the variables
increase together or go in opposite directions and the extent to which
the pattern is consistent across the data set.

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