Siegel-Tukey Test for Scale Differences

Both tests use rank sums evaluated against the Wilcoxon reference distribution, but they assign ranks in opposite ways. Mann-Whitney assigns ranks from smallest to largest (1, 2, 3, …) to detect location differences. Siegel-Tukey assigns ranks from the extremes inward (1 to the most extreme, 2 to the other extreme, 3 to the next most extreme, …) to detect spread differences. The two tests answer different questions and should not be used interchangeably.

Subtract each group's median from its own observations before pooling and ranking. This median-equalisation step removes the location shift so that any rank imbalance reflects spread alone. Some authors recommend using the grand median instead of group medians; the choice should be stated explicitly in the report.

Levene's test is generally more powerful when the data are approximately normally distributed, because it exploits the parametric structure. The Siegel-Tukey test is preferable when normality is clearly violated or the sample is small and you cannot confidently assess distributional shape. In practice many analysts run both and note whether they agree.

Yes. Because the test requires only a meaningful ordering of values — not interval-level measurement — it can be applied to ordinal scales. However, tied values are more common with coarse ordinal scales, and ties reduce the precision of the alternating rank assignment, so results should be interpreted with caution when many ties are present.