Northern Prairie Wildlife Research Center
We used a random-effects linear model to estimate the relative contributions of temporal and spatial components of variance. The model assumes that the value of the selected variable can be expressed as a linear combination of the above components in addition to a component for inherent variability. This analysis was complicated by not studying all areas in all years; variance components for study area and year are confounded with the interaction component. We recognized early this limitation in study design, but could not avoid it because we wanted to study more areas in total than could be evaluated in any single year. To minimize difficulties presented by the design, we divided study areas into 5 groups. One consisted of areas studied during both 1983 and 1984. A second was made up of areas studied during both 1984 and 1985. The remaining 3 groups included areas studied only in 1982, 1983, and 1985, respectively. This grouping allowed us to analyze balanced designs. A disadvantage is that the 2 areas studied in all years are included twice in the analysis.
We performed a 2-way (by study area and year) analysis of variance on each of the first 2 groups. For the 3 other groups, we did a 1-way (by study area) analysis of variance. The components of variance were estimated by equating mean squares with their expected values and solving for the unknown components (Searle 1971).
Because we performed an analysis on each of the 5 groups, we obtained 2 nearly independent estimates (from the first 2 groups) of each variance component associated with year and 5 of each associated with study area. These estimates were pooled by weighting each mean square by its degrees of freedom and averaging. Expected mean squares were obtained in a similar manner. The variance components were then estimated as before. Coefficients of variation (CV) of each component (Error = CVE, Study area = CVSA, and Year = CVY) were obtained by dividing the square root of the variance component by the mean of that variable.