Shift Function (Harrell-Davis Quantile Comparison)

The shift function compares two independent groups at several quantiles, usually the deciles, using Harrell-Davis quantile estimates and bootstrap inference to show where along the distribution they differ.

이동 함수는 두 독립 집단을 Harrell-Davis 분위수(보통 십분위)로 여러 지점에서 비교하고 부트스트랩으로 추론해 분포의 어느 부분이 다른지 보여 주는 방법입니다.

Two groups have similar means but I suspect the slow responders differ; how can I see which parts of the distributions differ?

두 집단 평균은 비슷한데 느린 응답자 쪽이 다른 것 같아요. 분포의 어느 부분이 다른지 볼 수 있나요?

Estimate each decile in both groups with the Harrell-Davis estimator and bootstrap the decile differences to get standard errors, p-values and confidence intervals. Adjusting the p-values across deciles with Hochberg's method shows which parts of the distribution differ.

When to use Shift Function (Harrell-Davis Quantile Comparison)

• You want to know whether groups differ in the tails, the centre or both.
• Distributions are skewed and a single mean comparison hides the pattern.
• Both groups have at least about 20 observations.

When to use something else

• You only need a single summary of location; use Yuen's trimmed means t test or the Mann-Whitney U test instead.
• The samples are paired; a dependent-groups shift function is needed instead.

Assumptions and requirements

• Two independent random samples.
• Continuous outcome with enough cases for stable tail quantiles.

What the analysis reports

• Harrell-Davis quantiles for each group and their difference (group 1 minus group 2)
• Bootstrap standard errors and percentile p-values
• Hochberg-adjusted p and confidence intervals at the Hochberg level for each quantile
• Number of significant quantile differences

How to report it

A shift function comparing Harrell-Davis deciles found [value] of 9 differences significant after Hochberg correction (percentile bootstrap, [value] resamples); the median difference was [value].

Related methods

• Two-Sample Kolmogorov-Smirnov Test
• Quantile Regression
• Yuen's Trimmed Means t Test

Run Shift Function (Harrell-Davis Quantile Comparison) on Quorant