  A sensitivity analysis in an observational study determines the magnitude of
bias from nonrandom treatment assignment that would need to be present to alter
the qualitative conclusions of a na\"{\i}ve analysis that presumes all biases
were removed by matching or by other analytic adjustments. The power of a
sensitivity analysis and the design sensitivity anticipate the outcome of a
sensitivity analysis under an assumed model for the generation of the data. It
is known that the power of a sensitivity analysis is affected by the choice of
test statistic, and, in particular, that a statistic with good Pitman
efficiency in a randomized experiment, such as Wilcoxon's signed rank
statistic, may have low power in a sensitivity analysis and low design
sensitivity when compared to other statistics. For instance, for an additive
treatment effect and errors that are Normal or logistic or $t$-distributed with
3 degrees of freedom, Brown's combined quantile average test has Pitman
efficiency close to that of Wilcoxon's test but has higher power in a
sensitivity analysis, while a version of Noether's test has poor Pitman
efficiency in a randomized experiment but much higher design sensitivity so it
is vastly more powerful than Wilcoxon's statistic in a sensitivity analysis if
the sample size is sufficiently large.
