Jackknife method for estimating the variance of the age composition using two-phase sampling with an application to commercial catches of swordfish (Xiphias gladius)

An estimate of the age composition of a commercial swordfish catch and its variance was obtained using the replicate full jackknife estimator for two-phase sampling where the sampling units in the first phase are clusters (vessel-trips) and the units of the second phase are individual fishes. The jackknife variance estimator was compared with an analytical estimator of variance commonly used in fisheries studies which ignores the clustering, and assumes simple random sampling of individual fish. The application of these naïve estimators to the Chilean South Pacific swordfish fishery results in an underestimation of the variance. This is a consequence of using an inappropriate primary sampling unit of analysis in the first-phase sample where the vessel-trip unit is replaced by an individual fish unit, thus ignoring the intra-cluster correlation in age samples. The jackknife estimator of variance is an alternative useful for complex two-phase sampling designs.