Are Survey Weights Needed? A Review of Diagnostic Tests in Regression Analysis

Researchers apply sampling weights to take account of unequal sample selection probabilities and to frame coverage errors and nonresponses. If researchers do not weight when appropriate, they risk having biased estimates. Alternatively, when they unnecessarily apply weights, they can create an inefficient estimator without reducing bias. Yet in practice researchers rarely test the necessity of weighting and are sometimes guided more by the current practice in their field than by scientific evidence. In addition, statistical tests for weighting are not widely known or available. This article reviews empirical tests to determine whether weighted analyses are justified. We focus on regression models, though the review's implications extend beyond regression. We find that nearly all weighting tests fall into two categories: difference in coefficients tests and weight association tests. We describe the distinguishing features of each category, present their properties, and explain the close relationship between them. We review the simulation evidence on their sampling properties in finite samples. Finally, we highlight the unanswered theoretical and practical questions that surround these tests and that deserve further research