ABSTRACT
In practical statistical work, it is seldom the case that a test statistic is used in the formal application of a test procedure, involving a rigid, uncritical comparison of the sample value of the statistic with the critical value, followed by an automatic decision for or against the null hypothesis. Often, in practical statistical work, several test statistics are applied to the same data, each followed by either formal acceptance or rejection of the hypothesis or computation of the p-value. Practical problems where the outcome of the observation is of dichotomous or binary type, 'success' or 'failure' say, are perhaps the most common. A monotonic transformation of a test statistic together with a corresponding transformation of the critical value does not change the partition of the sample space into acceptance and rejection regions, hence it does not change the test procedure.
