The practice of multiple significance testing is reviewed, and an alternative to the frequently used Bonferroni correction is considered. Rather than controlling the family-wise error rate (FWER)- the probability of a false positive in any of the significance tests-this alternative due to Benjamini and Hochberg controls the false discovery rate (FDR). This is the proportion of tests reporting a significant result that are actually 'false alarms'. The methods (and some variants) are demonstrated on a procedure to detect clusters of full-time unpaid carers based on UK census data, and are also assessed using simulation. Simulation results show that the FDR-based corrections are typically more powerful than FWER-based ones, and also that the degree of conservatism in FWER-based procedures is quite extreme, to the extent that the standard Bonferroni procedure intended to constrain the FWER to be below 0.05 actually has a FWER of around 6 x 10(-5). We conclude that in situations where one is scanning for anomalies, the extreme conservatism of FWER-based approaches results in a lack of power, and that FDR-based approaches are more appropriate.