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The size of perturbation that can be detected in the validation experiments will depend both on the change in the values of the measures as a function of misregistration and the standard error of those values. To quantify this, we define the sensitivity of a measure as follows.
where 84#84 is the value of the measure for some degree of deformation 79#79, 85#85 is the standare error of the estimate of 84#84. 86#86 is the change in 79#79 required for 84#84 to change by one noise standard error, which indicates the lower limit of change in misregistration 79#79 which can be detected by the measure. 87#87 is a function of 79#79; to simplify comparison between different methods of evaluation, we also use the mean sensitivity over a range of values of 79#79.
In order to compare the sensitivities of different methods of evaluation, we need also to estimate the expected error in 87#87. Since the validation experiments provided repeated estimates of 84#84, we can obtain empirical estimates of the errors in 84#84, 88#88, and 85#85. These can be combined, using error propagation, to estimate the uncertainty in the estimate of sensitivity.