Precision of Variable Sampling When the Response Variable and Inclusion Probabilities Are Not Highly Correlated

摘要

Variable probability sampling may be less efficient than simple random sampling if the response variable, y, is not highly positively correlated with the auxiliary variable, x, used to select the sample. Simulation results using binary and continuous response variables demonstrate quantitatively how much precision may be lost in this situation. Variable probability sampling may be less efficient for populations with correlations as high as .50, and efficiency relative to simple random sampling may be as low as 25-50% for low correlation populations.