The Box-Cox family of power transformations is widely used as a means for obtaining an approximate Gaussian distribution. In a regression setting, in which Y (or transformed Y) is regressed on a set of independent variables, the independent variables are usually assumed to be measured exactly, i.e., with no measurement error. In this paper we investigate the effect of measurement error in the independent variables (also known as errors-in-variables) on parameter estimation for the Box and Cox family of transformations (J. Roy. Statist. Soc. Ser. B 26, 1964). Ignoring measurement error in the independent variables causes biased parameter estimation in general. This conclusion is supported by analytical arguments and the results of simulation experiments. © 1995.