A method is specified for comparing the mean of a population of differences with zero or any other preassigned value. It may be applied to establish a difference between two treatments, where "treatment" should be understood in a wide sense, e.g. as a test method, measuring instrument or laboratory involved, and is applicable under the conditions that the series of differences can be considered as a series of independent random items and the distribution of the differences is normal or approximately normal. If the distribution deviates from the normal, it remains valid provided the sample size is sufficiently large (100 and more).