A note on a 'close pairs' test for space clustering.
Peter G. Smith, Malcolm C. Pike · Journal of Epidemiology & Community Health · 1974
Lloyd and Roberts (1973) have recently proposed in this journal a test for spatial clustering.For the 57 cases of congenital limb defects diagnosed in singleton births in Cardiff over the three-year period 1964-67, they calculated the total number of pairs, Z*, of cases whose places of residence at birth were less than a certain critical distance, d, apart.For comparison they took five control samples, each of size 57, drawn at random from the list of all singleton births in Cardiff during the same time period and, for each sample, they calcu- lated the number of 'close' pairs.The average number of close pairs in the control samples was then used to test whether there was an excess of such pairs among children with limb defects, the signifi- cance level being derived by assuming that the number of close pairs in the control samples was drawn from a Poisson distribution.We wish to point out here that the above test may be regarded as a special case of Knox's (1964) test, so that a randomization distribution of the number of close pairs may be defined and the expectation and variance under randomization of Z* may be easily derived.We also propose a method of analysis which is appropriate when a matched control sample (with matching, say, for social class) has been chosen.