Table 2.

1-D and 2-D fits of geometric constraints model predictions for different categories

Perspective	n	Passerines (1,064)			Nonpasserines (532)			Range size
								≤100 (756)			>100 (840)
		r2	ta=0	tb=1	r2	ta=0	tb=1	r2	ta=0	tb=1	r2	ta=0	tb1
1-D band mean
Latitude	55	0.58	−1.94	2.48	0.65	0.12	0.23	0.05	3.28	−3.03	0.68	−1.35	1.84
Longitude	68	0.60	0.01	−0.08	0.49	3.66	−3.25	0.00	1.71	−1.71	0.60	1.86	−1.71
2-D	1,742	0.18	2.32	−2.91	0.22	11.43	−11.90	0.02	12.57	−12.59	0.26	6.53	−6.69

Regression results from the geometric constraints model for different categories. Numbers in parentheses refer to numbers of species in the category. n is the number of observations for each test; t_a=0 is the t test statistic that indicates the deviation of intercept a from zero for the regression of observed versus predicted data (a measure of fit in magnitude); t_b=1 indicates the deviation of slope b of the regression from unity (a measure of fit in shape). t values in italics indicate a rejection of the tested hypothesis at the P = 0.05 level (two-tailed). Note that in this test as few as ten truly independent observations are sufficient to reject the null hypothesis for any t > 2.3 and not even over 10,000 observations can reject it for any t < 1.96.