Check a logistic scale before comparing reported variability

Define the task

A continuous logistic distribution is described by a location and positive scale. Its scale is not its standard deviation. When comparing two software outputs, retain the parameterization and units in the extraction table. Distinguish a distribution of continuous errors from the use of a logistic link in a binary-outcome regression.

Carry out the check

The continuous distribution has median and mean equal to its location and standard deviation equal to scale times pi divided by the square root of three. Its quartiles are location minus and plus scale times log(3). These identities offer independent checks without simulating a large sample.

Worked hypothetical example

For a hypothetical location of 10 and scale of 2 units, the SD is approximately 3.6276 and the interquartile range is approximately 4.3944. A value of 2 in an exported scale field should therefore not be relabeled as an SD. If a different program reports an SD of 2, convert it to scale 2 times the square root of three divided by pi before calculating probabilities. Specify which parameters were assumed and which were estimated.

Method checked 11 November 2026 against R documentation: The Logistic Distribution.