Robust Correlation Coefficients

Robust correlation coefficients, such as the percentage bend, winsorized, biweight midcorrelation and skipped correlations, measure linear association while limiting the influence of outlying or heavy-tailed observations.

Percentage bend, 윈저화, biweight 중간상관, skipped 상관처럼 이상값의 영향을 제한하면서 선형 관련성을 재는 상관계수입니다.

A few extreme points seem to drive my Pearson correlation. Which correlation should I report so that the result is not dominated by outliers?

몇 개의 극단값이 피어슨 상관을 좌우하는 것 같아요. 이상값에 휘둘리지 않는 상관계수는 무엇을 보고해야 하나요?

Report a robust correlation such as the percentage bend correlation or the biweight midcorrelation, which bend or down-weight extreme values in each variable, or a skipped correlation that removes bivariate outliers first. Compare it with Pearson's r: a large gap shows that a few observations were shaping the original estimate.

When to use Robust Correlation Coefficients

• Scatterplots show isolated points far from the main cloud.
• Variables have heavy tails but the relationship is roughly monotone or linear.
• You want a sensitivity check for a reported Pearson correlation.

When to use something else

• The relationship is clearly non-linear; use Spearman or Kendall rank correlation or a smoother instead.
• You need to adjust for covariates; use robust regression instead.

Assumptions and requirements

• Pairs of observations are independent.
• The association of interest is approximately linear in the bulk of the data.
• For the skipped correlation, outliers are detected by projection from a minimum covariance determinant centre.

What the analysis reports

• Robust correlation for each predictor with the outcome
• t statistic, degrees of freedom and p-value
• Percentile bootstrap confidence interval (not for the skipped correlation)
• Pearson r for comparison
• Number of outliers removed (skipped correlation)

How to report it

The percentage bend correlation (β = [value]) between [x] and [y] was r = [value], t([df]) = [value], p = [value], 95% bootstrap CI [[value], [value]] (Pearson r = [value]).

Related methods

• Pearson Correlation
• Spearman Rank Correlation
• Robust Location and Scale Estimates

Run Robust Correlation Coefficients on Quorant