Inflation of Type I error rate in multiple regression when independent variables are measured with error

When independent variables are measured with error, ordinary least squares regression can yield parameter estimates that are biased and inconsistent. This article documents an inflation of Type I error rate that can also occur. In addition to analytic results, a large‐scale Monte Carlo study shows unacceptably high Type I error rates under circumstances that could easily be encountered in practice. A set of smaller‐scale simulations indicate that the problem applies to various types of regression and various types of measurement error.