We are concerned with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a linear relation. A statistical test of this hypothesis is derived when the relation is specified with the exception of the additive constant. Then the result is reinterpreted in terms of the possible existence of an unspecified linear relation between true scores of two psychological tests. A numerical example is provided by way of illustration. (Author)