One group pretest-posttest design
The description ‘pre-experimental’ designs has been used to describe those designs that are so weak that it is difficult to draw any sound conclusions from the results. Perhaps the simplest of these that could be contemplated for serious study is the one-group pretest-posttest design, which can be represented as:
O1 X O2
where O1 represents pretest observations taken on a group experimental units, X represents an experimental intervention, and O2 represents posttest
observations taken on the same units. Here a major weakness is the absence of a separate control group, although under certain circumstances the change in observations between the pretest and the posttest might be considered a valid measure of the effect of the treatment.
One group pretest-negative-posttest designIn a design with O1 denoting an experimental site and X denoting experimental
attrition, one may represent this model:
O1 X O1∈X
where the ‘posttest’ observation is identical to its pretest condition, with X included. As stated earlier, X, a ‘zero functor’ that commits without difference, thereby more closely demonstrating a nonintervention than an intervention variable. Thus, the posttest is fundamentally (“radically”, in philosophical terms) negative (immanent) by the idempotence of pre-test conditions via X. This posttest negativity also is compounded by the inability to measure from a pretest after nonintervention by X. In more blunt, albeit paradoxical terms, X has already happened in the pretest, but linearly follows O1 in an experimental
design. Hence, attrition remains pre-experimental while proceeding with an experimental task. Perhaps this is by default of the language X used here to describe this.