Steel Many-to-One Rank Test

Steel's many-to-one rank test compares each treatment group with a single control using Wilcoxon rank sums from joint rankings of each pair, with simultaneous p-values from a multivariate normal approximation.

Steel 다대일 순위 검정은 각 처리군을 대조군과 함께 순위를 매긴 Wilcoxon 순위합으로 비교하고 다변량 정규 근사로 동시 p 를 구하는 방법입니다.

I have one control and three treatments with skewed outcomes; which treatments differ from the control?

대조군 하나와 처리군 셋이 있고 결과가 치우쳐 있어요. 어떤 처리군이 대조군과 다른가요?

Rank each treatment together with the control, standardise the treatment rank sum and adjust the p-values jointly using the correlation between the comparisons that share the control. It is the rank-based counterpart of Dunnett's test.

When to use Steel Many-to-One Rank Test

• Only comparisons against one control group are of interest.
• The outcome is ordinal or non-normal.
• You want familywise error control across the treatment-versus-control comparisons.

When to use something else

• All pairwise comparisons are needed; use Dunn's test instead.
• Data are approximately normal with equal variances; use Dunnett's test instead.

Assumptions and requirements

• Independent observations.
• Continuous outcome; the variance uses a tie correction but the correlation between comparisons assumes no ties.
• Group sizes large enough (about 5 or more) for the normal approximation.

What the analysis reports

• Rank sum W, its expectation and z for each treatment versus control
• Unadjusted and simultaneous (multivariate normal) adjusted p-values
• Median difference from control

How to report it

Steel's many-to-one test showed that [treatment] differed from the control, z = [value], adjusted p = [value].

Related methods

• Dunnett's Test
• Dunn's Test
• Kruskal-Wallis Test

Run Steel Many-to-One Rank Test on Quorant