Underestimation of Error in Wald-Bartlett Slope Estimation

1. Introduction and Summary Error variance may be employed to indicate the magnitude of measurement errors and is, hence, a valuable tool to the scientist. Error variance may be reliably estimated when two variables are each subject to random measurement error, if the variables are related by a single linear function, and if an unbiased estimate of the slope of that function is available. Techniques have been developed for computing a consistent estimate of the slope of the line describing the relationship between two variables, each subject to random measurement error (Wald, 1940). However, this paper shows that these techniques involve at least one sensitive assumption, the violation of which results in gross underestimation of error variance. This underestimation becomes progressively worse as error variance increases because the assumption is tenable only when the variance in the measurement error of the independent variable is very small. Consequently, error estimates based on such techniques will lead to overoptimistic conclusions irrespective of the accuracy of the measurements.