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RELATIONSHIPS OF BIRDS, LIZARDS, AND NOCT[.JRNAL RODENTS TO THEIR HABITAT IN TUCSON, ARIZONA Statistical Analysis Habitat ijariables. I defined associations between 15 of the habitat variables using Spearman ranked correlation analysis (Zar 1984, Statsoft 1995). 1 was restricted to 15 variables because several of the original variables were intended for descriptive purposes only and several others were not abundant enough to include. All 15 variables were retained for ensuing correlation analyses despite potential inter-correlations because I wanted to identify the association each habitat variable had with species abundances. Inter-correlated variables were not allowed to enter predictive models. The alpha level for this and all statistical tests was set at P <_0.05. Breeding Birds. Bird species and community variables generated at each census plot were: abundance of each species (averaged over the 4 visits), total abundance, and species richness for each of the following 3 groups of resident breeding birds: 1. Non-native species; 2. Native species; and, 3. A guild comprised of birds that were insectivorous, tree or shrub foliage gleaners, and shrub nesters. I selected feeding and nesting substrates as guild delineators to remove the subjectivity in guild selection that has been a major criticism of guild usage (see Holmes et al. 1979, Jaksic Y981, Johnson 1981, Severinghaus 1981, Verner 1984). I determined habitat associations for birds by Gamma correlation analysis of abundances of individual species with habitat variables. Fifteen ranked habitat descriptors were included with ranked abundances of 21 species of birds which met sample size requirements. I chose Gamma correlations because there were many ties in the bird abundance data, and this statistic takes ties into account, whereas Spearman and Kendall Tau coefficients do not (Statsoft 1995). Significant correlations with coefficients >_ 0.5 were retained. I then identified the relationship between each habitat variable and the bird species it correlated with by graphing mean bird species abundance against percent (or distance) classes of each habitat variable. I created classes that were meaningful to land managers and which evenly distributed data among groups. I used correlation and forward stepwise multiple regression to develop predictive habitat models for the 3 bird groups (Statsoft 1995). I used Spearman ranked correlation to determine associations between the bird community descriptors and habitat variables. Habitat variables that were correlated with species richness of each of the 3 bird groups were subjected to stepwise multiple regression analysis. I examined 4 residual diagnostics for each regression analysis. I plotted and removed outliers, which were defined as those cases whose standardized residuals were > 2 standard deviations from the mean residual value. Second, I evaluated Cook's distance (Cook 1977) for each case. Cook's distance is a measure of the affect a case has on the value of the regression coefficient and should be roughly equal for all cases. Third, I examined the Durbin-Watson statistic (Durbin and Watson 1951), which identifies whether cases are independent by analyzing the degree of correlation between adjacent residuals. Last, I reviewed both normal probability plots of residuals and plots of predicted versus residual scores. These indicate if residuals are normally distributed, and test the assumption of a linear relationship between the independent and dependent variables, respectively. I verified the predictive ability of each regression equation by cross validation (Meter et al. 1990). I randomly split the original data into 2 subsets. The equation for the predictive model was generated using 80% of the data, then this model was used to predict values for each case in the 20% subset. I determined the mean squared prediction error (MSPR) and compared it to the error mean square (MSE) of the original data subset. The closeness of these values indicated the extent to which the MSE was biased and gave an indication of how accurately the model should predict the value of the response variable using new data. In addition, I assessed the similarity of slopes in the 2 data subsets by comparing the residual scores between them using an independent samples t-test. If the slope of the second data subset differed from the first, then the scatter of data points would have had a different arrangement than that of the first; i.e., the residual values of the second subset would deviate more from the predicted slope than the residual values for the model building data set. L O ARIZONA GAME Fi FISH DEPARTMENT, TECH. REP. 20 SZEPHEN S. GERMAINE 1995