The propagation of errors in experimental data analysis: a comparison of pre- and post-test designs

Abstract

Experimental designs involving the randomization of cases to treatment and control groups are powerful and under-used in many areas of social science and social policy. This paper reminds readers of the pre- and post-test, and the post-test only, designs, before explaining briefly how measurement errors propagate according to error theory. The substance of the paper involves a series of comparisons using the same measurements, all assumed to have a small initial error, and seeing what would happen to that error in the two different experimental designs. The findings from these calculations and simulations are that although post-test only and pre- and post-test designs yield different ‘manifest’ results with the same data, the substantive conclusions drawn would be similar in most real-life situations. However, if these manifest results are assumed to be in error, stemming from small initial errors in the measurements at pre- and post-test, then these substantive conclusions could be completely wrong. In one example, the pre- and post-test designs propagate an initial maximum measurement error of 10% to an error of over 60,000% in the answer. In general, and perhaps counter-intuitively, the post-test only results are less misleading. The paper ends by summarizing the lessons drawn. The key message is that all other things being equal, the post-test only design is to be preferred. We may also need to use bigger samples, and more strictly accurate measures, capable of objective calibration focus on seeking larger effect sizes.