General Statistical Issues

The following papers, arranged in reverse chronological order, can be downloaded, as pdf files, by clicking on their titles.
In some cases, you can also access the associated journal site by clicking on the journal name.

Willett, J. B., and Singer, J. D. (1989). Caveats for the Statistical Consumer: A Cautionary Note on Case Weighting as a Method of Implementing Weighted Least-Squares..., Journal of Experimental Education, 57(3), 285-293

When no dedicated weighted least-squares procedure is available, mis-applying a case-weighting strategy as a method of implementing a weighted least-squares regression analysis can lead to gross inaccuracies. The magnitudes of many of the obtained estimates depend strongly on the absolute magnitudes of the weights applied during fitting and, in aaddition, several of the crucial regression estimates are incorrect. Among all possible rescalings, the most successful weights are those that have been rescaled so that they sum to the original sample size. However, even with the application of these rescaled weights, estimation of the residual variance remains problematic. A simple adjustment is provided.

Willett, J. B., and Singer, J. D. (1988). Another Cautionary Note R2: Its Use in Weighted Least-Squares Regression Analysis. American Statistician, 42(3), 236-238

Discusses problems with the R2 statistic when it is used in regression models that are fit by weighted least-squares. We show how a reliance on the R2 statistic can lead to an overly optimistic interpretation of the proportion of variance accounted for, in the regression. We propose a modification of the estimator and demonstrate its utility with an example.