TABLE 1.

Comparison of two statistical methods commonly applied to bivariate data (Cade and Noon 2003; Gotelli and Ellison 2004) and our proposed permutation test of no‐data zones. While the lines fit by quantile regressions can also be used to calculate the area extents of no‐data zones, the lines fit by linear regressions cannot.

	Linear regression	Quantile regression	Proposed permutation test of no‐data zones
Assumptions
Independent observations	Yes	Yes	Yes
Residuals ~ N	Yes	No	Not applicable
Linear response	Yes	No	No
Homoscedasticity	Yes	No	No
Sensitivity to outliers	Some	Limited	Potentially extreme
Core estimate/statistic	Slope of mean	Slope of quantile	Area (Q) of no‐data zone
Null hypothesis (H 0)	H 0: slope = 0	H 0: quantile slope = 0	H 0: $Q={\overline{Q}}_{\text{perm}.}$
p‐value meaning	P (slope|H 0)	P (quantile slope|H 0)	P (Q|H 0)
Appropriate as a boundary line method	No	Yes	Yes