Poorer postcodes within 5 regions in England have a lower responseto bowel-cancer screening invitations than do richer postcodes. Anextension of the sample-size formula for two proportions is usedto determine that needed to detect an increase in response rate thatvaries by deprivation quintile. The proportions plugged into theformula are weighted averages based on the relationship between responseand deprivation; the response rate is adjusted to be constant acrossdeprivation quintiles. From a baseline period between October 2006and January 2009, detection of an absolute or relative increase ofat least 1,2,3,4 and 5% in response rate is required for the richestto poorest quintiles respectively because the interventions werechosen as those most likely to have an effect in the lower socioeconomicgroups. A computer simulation experiment shows that the approachis more conservative than a likelihood-ratio calculation, and itappears sensible when compared with repeated application of a two-samplecalculation at each quintile.