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Part I: Vital Statistics about Statistics

No matter how large a sample is, if it’s based on non-random methods, the
results will not represent the population that the researcher wants to draw
conclusions about. Don’t be taken in by large samples — first check to see how
they were selected. Look for the term random sample. If you see that term, dig
further into the fine print to see how the sample was actually selected and use
the preceding definition to verify that the sample was, in fact, selected ran-
domly. A small random sample is better than a large non-random one.
Statistic
A statistic is a number that summarizes the data collected from a sample.
People use many different statistics to summarize data. For example, data
can be summarized as a percentage (60% of U.S. households sampled own
more than two cars), an average (the average price of a home in this sample
is . . .), a median (the median salary for the 1,000 computer scientists in this
sample was . . .), or a percentile (your baby’s weight is at the 90th percentile
this month, based on data collected from over 10,000 babies).
The type of statistic calculated depends on the type of data. For example,
percentages are used to summarize categorical data, and means are used to
summarize numerical data. The price of a home is a numerical variable, so
you can calculate its mean or standard deviation. However, the color of a
home is a categorical variable; finding the standard deviation or median of
color makes no sense. In this case, the important statistics are the percent-
ages of homes of each color.
Not all statistics are correct or fair, of course. Just because someone gives you
a statistic, nothing guarantees that the statistic is scientific or legitimate. You
may have heard the saying, “Figures don’t lie, but liars figure.”
Parameter
Statistics are based on sample data, not on population data. If you col-
lect data from the entire population, that process is called a census. If you
then summarize the entire census information from one variable into a
single number, that number is a parameter, not a statistic. Most of the time,
researchers are trying to estimate the parameters using statistics. The U.S.
Census Bureau wants to report the total number of people in the U.S., so it
conducts a census. However, due to logistical problems in doing such an
arduous task (such as being able to contact homeless folks), the census num-
bers can only be called estimates in the end, and they’re adjusted upward to
account for people the census missed.

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