124 USGS/BRD/ITR-2000-0012 



confidence limits; (3) the r 2 value; and (4) the p-value 

 for testing whether the slope was statistically different 

 from zero. In Figures 2.4, 2. 1 0, and 2. 1 2, Sum Regression 

 lines are indicated for trends that were statistically 

 different from zero at the 0.05 significance level. 



To perform Poisson Regressions, we summed 

 available data from individual colonies within colony 

 complexes in central California and Washington from 

 Appendixes C, D, F, and G (Tables H-3 and H-4). The 

 regressions were conducted by examining the relation 

 of N on year where N is the sum of whole-colony counts 

 for all colonies in a colony complex, and using the 

 deviance to adjust the standard errors for overdispersion 

 (McCullagh and Nelder 1989; SAS 1997). We described 

 Poisson Regressions for three time periods by presenting 

 in Tables H-5 and H-6: (1) the slope of ln(AO for each 

 colony complex with standard error and 95% Bonferroni 

 simultaneous confidence limits; (2) the percent per 

 annum change for each colony complex, with 95% 

 Bonferroni simultaneous confidence limits; (3) the 

 Bonferroni-adjusted p-values for testing whether the 

 slopes were significantly different from zero (Westfall 

 and Young 1993); and (4) results of testing for 

 differences between trends for different colony 



complexes. In Figures 2.3 and 2. 1 1 , Poisson Regression 

 lines are indicated at colony complexes with trends that 

 were statistically different from zero at the 0.05 

 significance level under Bonferroni adjustments for 

 simultaneous inference across colony complexes in 

 central California and Washington. 



We performed Route Regressions by taking the 

 averages of percent per annum changes from Poisson 

 Regressions for colony complexes within geographic 

 areas (weighted by population size and survey effort). 

 Standard errors were obtained by bootstrap (Efron and 

 Tibshirani 1993). Both Sum Regression and Route 

 Regression methods aim to estimate trends for 

 geographic areas. However, Route Regression better 

 accounts for between-site variation in trends when study 

 sites are randomly sampled, thus often producing a more 

 reliable test and confidence interval for trend, but does 

 not produce an estimate of intercept. In Table H-7, we 

 compared trends depicted with Sum Regressions and 

 Route Regressions in central California, which helped 

 to assess the general consistency of the Sum Regression 

 methods used to derive population trends for central 

 California. 



