Incorporating sampling variance which may be zero into ANOVA and REML: analysis of a waterfowl activity study
by
Graham Hepworth
Department of Mathematics & Statistics, The University of Melbourne
Coauthors: Andrew Hamilton (School of Environmental and Information Sciences, Charles Sturt University)

A major sewage treatment facility near Melbourne is listed as a wetland of international importance for the significant numbers of waterfowl found there. A study was conducted at one of the facility’s ponds to estimate the proportion of birds engaged in various activities (feeding, resting, etc.) at five different times of the day. The activities of the birds were observed using "scan sampling", in which a telescope is scanned through a particular angle. Samples were taken weekly for about a year, and then monthly for another year.

Estimating the proportions on each sampling occasion, and their associated sampling variance, was complicated by the fact that birds in close proximity to each other were more likely to be engaged in the same activity than those further apart. In addition, on some occasions there were too many birds to observe, and a sub-sample was taken. This resulted in data for which some of the observations had an associated sampling variance of zero, and some had a non-zero value.

It was of interest to compare the mean proportions for the five times of day. This necessitated incorporating sampling variance which could be zero into the analysis. This was not feasible with ANOVA because of the impossibility of weighting zero variances. It was achieved in REML by adding the sampling variance to the other sources of variance, using the flexibility of Genstat.

Date received: August 29, 2002