The aim of this research is to investigate the sensitivity of a selection of inferential test statistics to small perturbations in the data, in particular perturbing the data within its reported accuracy. The method used is that proposed by O'Brien (1975) which considers the sensitivity of econometric estimators. This approach involves constructing the first term of a Taylor series expansion in terms of the data points for any sample statistic, in our case the inferential statistic of interest. This provides a linearized approximation to the perturbation in the sample statistic. If we assume that the perturbations are uniformly distributed this linear approximation will be approximately normally distributed and its standard deviation can be used as a measure of sensitivity. The usefulness of this measure can be investigated by a Monte Carlo simulation using the linear approximation as a control variable for the perturbed sample statistic. We consider statistics taken from the model selection procedure, namely the Durbin-Watson, F. test, Lagrange Multiplier test for serial correlation and the COMFAC procedure. Simulations are performed on the data sets used by Henry (1974), Longley (1967) and Hendry and Mizon (1980). These suggest that the measure proposed does indeed provide a useful indicator of the sensitivity of the statistic. However none of the statistics exhibited great sensitivity in relation to the critical value for rejection of the hypothesis in question. One of the main drawbacks for the application of this measure in empirical work is that it relates to the original data set. Most empirical work uses transformed data which has to be accounted for when forming the measure of sensitivity - often not a trivial task.