User:Stephen.floor/Cliff's delta

Cliff's delta

Cliff's delta or $d$ is a statistical measure of effect size, or how different two distributions are. It was originally developed by Norman Cliff for use with ordinal data. In short, $d$ is a measure of how often one the values in one distribution are larger than the values in a second distribution. Crucially, it does not require any assumptions about the shape or spread of the two distributions.

The sample estimate $d$ is given by:

$d={\frac {\#(x_{i}>x_{j})-\#(x_{i}<x_{j})}{mn}}$

where the two distributions are of size $n$ and $m$ with items $x_{i}$ and $x_{j}$, respectively, and $\#$ is defined as the number of times.

$d$ is a linear transformation of the Mann-Whitney U statistic, however it also captures the direction of the difference in its sign. Given the Mann-Whitney $U$, $d$ is:

$d={\frac {2U}{mn}}-1$

The R package orddom calculates $d$ as well as bootstrap confidence intervals.

External links

• The orddom R package at CRAN