Assume (as in the case of measurements produced by two well-calibrated measuring instruments) the means of two populations are equal. Use the Wilcoxon rank sum statistic for testing hypotheses concerning the population variances as follows:
a. Rank the combined sample.
b. Number the ranked observations "from the outside in"; that is, number the smallest observation 1, the largest 2, the next-to-smallest 3, the next-to-largest 4, and so on. This sequence of numbers induces an ordering on the symbols A (population A items) and B (population B items). If σA2 σB2, one would expect to find a preponderance of A's near the beginning of the sequence, and thus a relatively small "sum of ranks" for the A observations.
c. Given the measurements in the table produced by well-calibrated precision instruments A and B, test at near the a α .05 level to determine whether the more expensive instrument B is more precise than A.

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Instrument A 1060.21 1060.34 1060.27 1060.36 1060.40 Instrument B 1060.24 1060.28 1060.32 1060.30