Truncated sequential sign tests for location shift

A truncated sequential sign test for location shift is studied when the null or target location has been estimated from a prior, fixed sample. If the randomness of the target is ignored then the test is shown to be strongly anticonservative, the degree being proportional to the ratio of the truncation point to the fixed sample size. The test is distribution-free under the hypothesis of no shift enabling exact Type I errors and null expected samples sizes to be calculated and compared to a modified Brownian motion approximation. A Monte Carlo power study shows that the test compares favorably with thr test against a Xnown target. An abbreviated table of critical values is given.