Permutation Tests. With the advent of high-speed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Permutation tests constitute one such collection of new procedures. To perform a permutation test to compare two population means using independent samples, proceed as follows.

1. Combine the two samples.

2. Randomly select n1 members from the combined sample. Now treat these n1 members as the first sample and the remaining n2 members as the second sample.

3. Compute the difference between the means of the two new samples.
4. Repeat steps 2 and 3 a large number (hundreds or thousands) of times.
5. The distribution of the resulting differences between sample means provides an estimate of the sampling distribution of the sample-mean differences when the null hypothesis of equal population means is true. This estimate is called a permutation distribution.
6. The (estimated) P-value of the hypothesis test equals the proportion of values of the permutation distribution that are as extreme as or more extreme than the difference between the two observed sample means.
Refer to Example 10.3 on page 471. Use the technology of your choice to conduct a permutation test and compare your results with those found by using the pooled t-test. Discuss any discrepancy that you encounter.