Randomization Tests (4 of 6)

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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.
 X  Y
 4  3
 8  5
 2  1
10  7
 9  8
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.
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