Two approximate ancillaries, the Efron-Hinkley ancillary and the (signed) likelihood ratio, are compared in a specific example by means of their level curves, their marginal densities and the conditional and unconditional likelihood functions. It is shown that in the present model the latter of the two ancillaries is the better. It is almost exactly distribution constant and has more stable conditional likelihood functions.
"A Comparison of the Efron-Hinkley Ancillary and the Likelihood Ratio Ancillary in a Particular Example." Ann. Statist. 9 (6) 1328 - 1333, November, 1981. https://doi.org/10.1214/aos/1176345649