Many animals, including humans, tend to live in groups, herds, flocks, bands, packs, shoals, or colonies (hereafter: groups) of conspecific individuals. The size of these groups, as expressed by the number of participant individuals, is an important aspect of their social environment. 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. Unfortunately, group size measures are notoriously hard to handle statistically since groups size values typically exhibit an aggregated (right-skewed) distribution: most groups are small, few are large, and a very few are very large.
Statistical measures of group size roughly fall into two categories.
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As Jarman (1974) pointed out, average individuals live in groups larger than average – simply because the groups smaller than average have fewer individuals than the groups larger than average. (Except for an unrealistic case when all groups are of equal size.) Therefore, when we wish to characterize a typical (average) individual’s social environment, we should not apply the outsiders’ view of group size. Reiczigel et al. (2008) proposed the following measures:
Due to the aggregated (right-skewed) distribution of group members among groups, the application of parametric statistics would be misleading. Another problem arises when analyzing crowding values. Crowding data consist of nonindependent 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.)
The paper by Reiczigel et al. (2008) discusses the statistical problems associated with group size measures (calculating confidence intervals, 2-sample tests, etc.) and offers a free statistical toolset (Flocker 1.1) to handle them in a user-friendly manner.
Size of groups, organizations, and communities