scrdsp

A risk score’s spread across groups

R

scrdsp(score, group = NULL, ref = NULL, conf = 0.95)

Each group’s number of cases, mean, median and standard deviation of a score, each mean’s gap to a reference group with its interval, and the one-way analysis of variance of the score on group, with Welch’s (1951) test, which does not assume equal variances.

Parameters

score

The scores: finite numbers, one per case. A clpre list from clprep() is taken too: its elements fill the arguments by name.

group

The group of each case: labels.

ref

The reference group: NULL for the group with the lowest mean (the first on ties), its label, or its position from 1.

conf

The confidence level of the intervals, strictly between 0 and 1.

Returns

A list: tab, a data frame with one row per group: group, n, mean, median, sd (NaN for one case), gap, se, lo and hi (NaN for the reference); anova and welch, named vectors f, df1, df2 and p; spread (the largest mean minus the smallest); ref.

Notes

The analysis of variance is the standard one (stats::anova() of stats::lm()): a group with one case adds to the between-group sum of squares and nothing to the within-group one. The gaps’ intervals use the pooled within-group variance on its degrees of freedom. Welch’s test needs two or more cases and some spread in every group, and is NaN otherwise.

A gap in mean scores is not by itself a sign of bias: a score built to predict an outcome differs between groups whose rates of that outcome differ. Read it with calaud(), which compares the scores with what was recorded, or fair(), which compares them with outcomes case by case.

References

Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3-4), 330-336. doi:10.1093/biomet/38.3-4.330

Examples

set.seed(7)
g <- rep(c("x", "y", "z"), c(40, 40, 20))
s <- rnorm(100, ifelse(g == "x", 0, ifelse(g == "y", 0.5, 1)))
scrdsp(s, g)

Also in the R reference, with the method and its source.