Cavity Size and Use, Biologists freely discuss the concept of competition between species, but it is difficult to measure. In one study of competition for nesting cavities in Southeast Colorado, Donald Youkey (Oregon State University Dept. of Fisheries & Wildlife) located nearly 300 cavities occupied by a variety of bird and rodent species. Display 5.22 shows box plots of the entrance area measurements from cavities chosen by nine common nesting species. The general characteristics-positive skewness, larger spreads in the groups with larger means-suggest the need for a transformation. On the logarithmic scale, the spreads are relatively uniform, and the summary statistics appear in Display 5.23. Are the species competing for the same size cavities? Or, are there differences in the cavity sizes selected by animals of different species? It appears that there are two very different sets of species here. The first six selected relatively small cavities while the last three selected larger ones. Is that the only significant difference?

(a) Compute the pooled estimate of variance.
(b) Construct an analysis of variance table to test for species differences (The sample standard deviation of all 294 observations as one group is SD D 0 4962.) Perform the F -test.
(c) Verify that the analysis of variance method for calculating the between-group sum of squares yields the same answer as the formula.

(d) Fit an intermediate model in which the first six species have one common mean and the last three species have another common mean. Construct an analysis of variance table with F -tests to compare this model with (i) the equal-means model and (ii) the separate-means model. Perform the F -test.

Transcribed Image Text:

DISPLAY 5.22 Box plots for areas of entrances to cavities used by different species 12 11 - 10 Species: Mouse Pinyon Bewick's Mountain Ash- Plain Northern Westem Americ mouse wren bluebird throated titmouse flicker Screech- kestre flycatcher owl 127 44 24 41 18 16 11 6. n: Cavity Entrance Area (1,000 mm2) 4) Between-group SS =E"T;² – nF°. i=1