The mean or average value of a measure or indicator variable used to monitor
a fish population can be defined in various ways, each with a
correspondingly different statistical estimator for use in the context of a
trawl survey. When, as is typical for many species, fish are heterogeneously
clustered over space, then scooped in clusters from restricted localities
using a trawl, these different estimators can produce different sample mean
values with contrasting variations over time, possibly leading to different
inferences about the fish population. Two mean parameters and their
intuitive estimators, the mean “over fish”, and the mean “over stations”,
are discussed and found to present contrasting statistical properties. A
third estimator based on fitting a mixed model is proposed which has
intermediate properties based on the within-haul correlation. The three
estimators are applied illustratively to length data for cod caught in the
North Sea by the English groundfish survey from 1992 to 2007. The time
series of the mean over stations was smoothest, that for the mean over fish
much more variable, and the mixed mean fell between in all years. Variance
estimators derived from the fitted mixed model are also put forward.
Estimates made from the example suggested that the mixed mean is most
efficient. The type of estimator used for the mean should always be
considered carefully and mentioned when reporting indicator studies.