However, analysts must be wary of accepting that the data suggest a real change, as randomly occurring events tend to cluster together, resulting in a preponderance of shorter intervals even if the underlying rate is unchanged. Examination of an apparent clustering of rare but serious events is useful to identify real, nonrandom changes in the rate of these events and to recognize whether or not contagious effects are operating. Four sets of epidemic-like data (from events occurring in Great Britain) are presented: absconds from open Youth Custody Centers, incidents of self- injury in a women's prison, suicides at a local prison, and fires at a dispersal prison. Various ways of examining the data, and potential pitfalls for statistical analysis, are described. 12 figures