Measurement Error and Statistical Significance of an Independent Variable

The well-known result that measurement error in an independent variable biases the least-squares estimator of that variable's regression coefficient towards zero is insufficient information to determine the effect of measurement error on the standard t test of the null hypothesis that the coefficient equals zero.This note shows that measurement error tends to lower the probability of rejecting such a null hypothesis by inducing a lower limiting value of the coefficient's t statistic.This result holds despite an ambiguous effect of measurement error on the coefficient's estimated standard error.