Randomization Tests (4 of 6)
Consider one more example of a randomization test. Suppose a
researcher wished to know whether or not there were a relationship
between two variables: X and Y. The most common way to test the
relationship would be using Pearson's r
The test based on the principle of randomization would proceed as
follows. First, Pearson's correlation would be computed for the data
as they stand. The value is: r = 0.9556. Next, the number of ways the
X and Y numbers could be paired is calculated (Note that X's do not
become Y's and Y's do not become X's. It is the pairings that
change.) The formula for the number of ways that the numbers can be
paired is simply:
W = N!
where N is the number of pairs of numbers.
For this example, N = 5 and W = 120. This means there are 120 ways
the numbers can be paired. Of these pairings, only one would produce
a higher correlation than 0.9556. It is shown on the next page.
Therefore, there are two ways of arranging the data that result in
correlations of 0.9556 or higher.