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Figure 1.6 (a) Positions of the 10 points of the numerical example with respect to variables xj and x2.

(b) Frequency histogram of the (1 + 999) permutation results (t statistic for correlation coefficient); the reference value obtained for the points in (a), t = 2.78456, is also shown.

There are 10! = 3.6288 x 106 possible permutations of the 10 values of variable xj (or x2). Here, 999 of these permutations were generated using a random permutation algorithm; they represent a random sample of the 3.6288 x 106 possible permutations. The computed values for the test statistic (t) between permuted xj and fixed x2 have the distribution shown in Fig. 1.6b; the reference value, t = 2.78456, has been added to this distribution. The permutation results are summarized in the following table, where '|t|' is the (absolute) reference value of the t statistic (11 \ = 2.78456) and 't*' is a value obtained after permutation. The absolute value of the reference t is used in the table to make it a general example, because there are cases where t is negative.