Intercluster correlations for binomial data: An application to Seed Testing

Certification of crop seeds from a seed lot requires determination of the seed germination rate through tests governed by the International Seed Testing Association (ISTA) and the Association of Official Seed Analysts (AOSA). The results from four tests of 100 seeds each are compared with published tolerances to determine whether seed lots concur with a labeled germination rate. Examination of results from numerous corn and soybean seed lots sent to more than 30 member laboratories of the AOSA and the Society of Commercial Seed Technologists (SCST) suggested that, in aggregate, counts reported by the laboratories frequently show less sample variability than expected under independentbinomial sampling due to positive correlation among the individual test results. Whereas much of the recent literature on correlated binomial data is concerned with efficient methods for estimating the binomial success probabilities, comparatively little attention is paid to the problem of diagnosing whether correlations exist and are significant. Considering the replicate tests as clusters, we propose an estimator for the intercluster (interreplicate count) correlation coefficient and examine its statistical properties. Results from applying the estimator in unblinded and blinded seed tests are presented. The results are revealing; the estimates tend to be larger and significant in the unblinded seed tests.