Many phenotypic traits show plasticity but behaviour is often considered the 'most plastic' aspect of phenotype as it is likely to show the quickest response to temporal changes in conditions or 'situation'. However, it has also been noted that constraints on sensory acuity, cognitive structure and physiological capacities place limits on behavioural plasticity. Such limits to plasticity may generate consistent differences in behaviour between individuals from the same population. It has recently been suggested that these consistent differences in individual behaviour may be adaptive and the term 'animal personalities' has been used to describe them. In many cases, however, a degree of both behavioural plasticity and relative consistency is probable. To understand the possible functions of animal personalities, it is necessary to determine the relative strength of each tendency and this may be achieved by comparison of statistical effect sizes for tests of difference and concordance. Here, we describe a new statistical framework for making such comparisons and investigate cross-situational plasticity and consistency in the duration of startle responses in the European hermit crab Pagurus bernhardus, in the field and the laboratory. The effect sizes of tests for behavioural consistency were greater than for tests of behavioural plasticity, indicating for the first time the presence of animal personalities in a crustacean model.