Glossary of Statistical Quantities Appearing in `Hmisc` and `rms` R Output

`Hmisc` Package

Gmd: Gini’s mean difference, a measure of dispersion defined as the mean absolute difference over all possible pairs of different observations. It is more robust than the standard deviation.

Info: Information index, a measure of the information content in a numeric variable relative to the information in a continuous numeric variable with no ties. The lowest value of Info occurs in a very imbalanced binary variable. Info comes from the approximate formula for the variance of a log odds ratio for a proportional odds model/Wilcoxon test, due to Whitehead 1993. Info is the ratio of the variance if there no ties in the data to the variance from the frequency distribution of observed values. Info near 1.0 means that the power of a Wilcoxon test comparing values of the variable between two groups is as good as the power for testing a continuous variable with no ties, effect sizes being equal. See this and this for more information and discussion.

pMedian: Pseudomedian, a robust and efficient measure of central tendency (distribution location) defined as the median of all possible pairwise averages of values, including pairs where an observation is averaged with itself. The pseudomedian is also called the Hodges-Lehmann one-sample estimator and is the location parameter that corresponds to what the Wilcoxon signed-rank test is testing. When the distribution is symmetric, the mean, median, and pseudomedian coincide. The pseudomedian is more stable and precise than the median. When the data come from a normal distribution, the efficiency of the pseudomedian compared to the sample mean for estimating the population mean is \(\frac{3}{\pi} = 0.955\). The efficiency of the sample median is only \(\frac{2}{\pi} = 0.637\) for estimating the population mean.