COMMON MISTEAKS MISTAKES IN
USING STATISTICS: Spotting and Avoiding Them
What is a Random Sample?
Sources of Confusion
Many people misunderstand what the phrase "random
sample" means. There are two reasons why this is the case.
First, the word "random" in the phrase "random sample" does not have its ordinary,
everyday meaning -- that is, does not
refer to the first definition you
would find in a dictionary. Here are the first definitions from a
couple of dictionaries:
One common mistake
arises from applying this ordinary, everyday
meaning of "random" to the phrase "random sample"1
is concluding that a
sample is not random because it has a pattern. In fact, a
(using the technical meaning of the phrase) might have a pattern (or it might
not). In fact, there is no way we
can tell from looking at the sample whether or not it qualifies as a
random sample. 2
"Having no specific
or objective; haphazard" (The
American Heritage Dictionary, Second College Edition, Houghton
without definite aim, reason, or pattern (Dictionary.Com,
http://dictionary.reference.com/browse/random, accessed 11/19/09)
This brings up the second reason why the phrase is often misunderstood:
The adjective "random" refers to the
method by which the sample is chosen. Thus the phrase "random sample" really
means "randomly chosen sample."
The next sections elaborate on what "randomly chosen" means.
1. Adding to the confusion, the dictionary definition may apply in the phrases "random
process" and "random variable"; see Note 1 in Example 6 on the page Random Variables and Probability Distributions
for an example.
2. Many "tests of
strings of numbers have been developed. However, none of them is
perfect; they can just help screen out some strings that are not
random. Often a "suite" of such tests is used to check "random number
generators". See Turiel, Thomas (2007), Quantum Random Bit Generators,
The American Statistician, v.
61 no. 3, pp. 255 - 259, for further
discussion and references.
3. W. Edwards Deming, in his obituary of Walter
reflects this idea, saying, "There was to Shewhart no such thing as a
random sample. There was and is, however, such a thing as a sample
selected by a random operation." (Quoted from p. 20 of an excerpt
of the obituary that appeared in Amstat
News, September, 2009. The original article appeared in The American Statistician, v. 21,
pp. 39 - 40.) Shewhart defined a random sample as "A sample drawn
under conditions such that the Law of Large Numbers applies" (p. 256)
in his article Random Sampling, The American Mathematical Monthly, Vol.
38, No. 5, May, 1931, pp. 245 - 270.
Updated August 28, 2012