Is the Logic of the T-test for Two Independent Samples Fallacious? An Analysis of the Ontological Status of the Treated Population

The t test for two independent samples is an inferential statistic used to examine the difference between two population means, which in tum correspond to the means of two independent samples. An ontological argument is formulated whereby it is contended that a "treated population" is exclusively an abstract idea and, thus devoid of a referent in the external world. In philosophically orientated terminology, it is shown that a treated population is an imaginary population that is reified and thereby erroneously accorded the status of a concrete particular. It is argued that this reveals an obvious internal tension with regards to the logic of the t test for two independent samples when applied in the case of an experimentally manipulated independent variable. A potential solution is advanced.