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Abstract
The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray the sensitivities of certain goodness-of-fit statistics to minor perturbations in the assumed distribution.