Group size measures

Group size tend to be highly variable even within the same species, thus we often need statistical measures to quantify group size and statistical tests to compare these measures between two or more samples.

Therefore, when we wish to characterize a typical (average) individual's social environment, we should apply non-parametric estimations of group size.

Crowding data consist of non-independent values, or ties, which show multiple and simultaneous changes due to a single biological event.

(Say, all group members' crowding values change simultaneously whenever an individual joins or leaves.)

Reiczigel et al. (2008) discuss the statistical problems associated with group size measures (calculating confidence intervals, two-sample tests, etc.)

A group acts as a social environment of individuals: a flock of nine common cranes .
Colony size measures for rooks breeding in Normandy. The distribution of colonies (vertical axis above) and the distribution of individuals (vertical axis below) across the size classes of colonies (horizontal axis). The number of individuals is given in pairs. Animal group size data tend to exhibit aggregated (right-skewed) distributions , i.e. most groups are small, a few are large, and a very few are very large. Note that average individuals live in colonies larger than the average colony size. (Data from Normandy, 1999-2000 (smoothed), Debout, 2003)