On a truncation-flexible repeated significance test

A repeated significance test for the mean of a normal distribution with guaranteed Type I error rate not depending on the truncation point is presented. The type of design has the advantage that it may be applied to define a sequential test based on accumulating data, applicable to a wide range of variables of which the fixed-sample-size test would have been based on the standard normal, without the requirement that the covariance structure of the sequence by computed explicitly. The test is shown to be especially convenient for certain types of ongoing survival studies, and for the problem of testing for differences in means or proportions, and appears to have operating characteristics similar to those of standard repeated significance tests with corresponding truncation points.