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COMMON MISTEAKS MISTAKES IN
USING STATISTICS: Spotting and Avoiding Them

# Why Is Random Sampling
Important?

The myth: "A random
sample
will be
representative of the population".

In fact, this
statement is false -- a random sample might, by chance, turn
out to be anything but representative. For example, it is possible
(though unlikely) that if you toss a fair die ten times, all the tosses
will come up six. If you find a book or web page
that gives this reason, apply some healthy skepticism to other things
it claims.

A slightly better explanation that is
partly true but partly urban legend :
"Random sampling eliminates bias by
giving all individuals an equal chance to be chosen."^{1
}
It is true that sampling
randomly
will eliminate systematic bias. Moreover, this statement is often the
best plausible explanation that is acceptable to someone with little
mathematical background. However, this statement could easily be
misinterpreted as the myth above. Moreover, there is an additional,
very important, reason why random sampling is important, at least in
frequentist statistical procedures, which are those most often taught
(especially in introductory classes) and used.^{
}

The real reason: The mathematical theorems which justify
most
frequentist statistical procedures apply only to random samples.

1. Moore and McCabe
(2006),
Introduction to the Practice of Statistics, Third edition, p. 219. The
quote and discussion here should not be taken as criticism of the book
-- it is one of the best introductory textbooks for a wide audience.