The classical problem of pooling data for several intraclass correlation coefficients is considered when independent samples are drawn from multivariate normal populations. The decision whether to pool several samples or not is based on the outcome of the shrinkage pretest estimator (SPE). The asymptotic properties of the SPE in the light of quadratic loss function are investigated. Further, it is demonstrated that the proposed shrinkage pretest estimator provides a wider range of values of the non-centrality parameter than the usual pretest estimator in which it dominates the classical estimator of correlation parameter vector.