Assume, I want to evaluate how effective two teachers are in teaching English to German children. Both teachers have been teaching at the same high school for twenty years, and both use a distinctly different pedagogical methodology. In fact a small competition has arisen between them: they have published and discussed their ideas and practise in journals relevant to their profession, and they have now called in a data analyst (you) to conduct this evaluation which, so they hope, will decide their contest and reconcile the former friends.
The school, where they both work, is the only school for its small town. When pupils enter this school, they are randomly assigned classes by name: all children are ordered alphabetically by last name, and the firstone half (A to median)of the children are assigned to one class (and one maths teacher), the secondother half of the children (median to Z) to the other class (and the other maths teacher). For all intents and purposes, the assignment is random, since the first letter of the last name does not, to anyones knowledge, correlate with anything that is psychologically relevant.
The two teachers are tired of not knowing which method is best. In the interest of their pupils they want to finally decide on the better one and both use this from now on. They hope, that you don't need to test one cohort of children when they finish elementary school, have them taught for the 8 years from 5th grade until they graduate from high school, and then measure their mathematical ability again, to come to a conclusion. Therefore they ask you:
Is it enough to compare the levels of the dependent variable post-intervention? Or do you need to measure it pre-intervention as well? Why?