Project Star

Project STAR (Student to Teacher Achievement Ratio) was a fully randomized trial to examine the effect of class sizes for students in Kindergarten through Grade 3. The experiment was run over 79 public schools in Tennessee in the late 1980's. The treatment here was class size, with these being a small class size or regular class size with a teacher as well as supplementing the regular class size with a teachers aide. Teachers and students were randomly assigned to the classrooms. The outcome variable of interest were standardized test scores (math and literacy).

This is clearly an experiment, but as with many real world experiment we do not have perfect randomization and measurement. First, the experiment covered a number of years and in this time people move etc. and so students dropped out of the study. As we have seen with representativeness, if the selection of the dropouts is independent of the assignments to classes this would have no effect (because performance conditional on staying would equal performance). There were also students moved for other reasons, most likely discipline. Researchers working with these data spend some effort (including construction statistics) to try and show that there is no effect here. Unlike phone polls we do observe characteristics of the dropouts.

A secondary issue with representativeness is that if we want to take these results as indicative of what happens over the entire country, then we need to argue that these schools and students are representative of the country as a whole. The racial makeup of the students was similar to the US as a whole, however clearly there will be regions of the US that have racial differences to Tennessee. Further, on average the families of the participants were poorer than national averages.

However this was a very carefully run experiment, and the results have been considered insightful for the question of the impact of class size. It is not surprising that there is a positive effect of having fewer students per teacher. However it is important to quantify this effect to examine if the reduction in class sizes is worth the cost of doing it. The results suggest that smaller class sizes are a reasonable investment from an economic perspective, in particular for black students. A detailed overview using regression analysis (which we do not cover here) can be found here.

Further work has shown longer term improvements of smaller class sizes. Since the experiment was run some time ago, the participants have grown up and had at least the start of their working lives. One study attempts to examine the earnings outcomes and long term education outcomes of the students in the study. They find that an increase of one percent in the end of Kindergarten test scores results in about an extra $100 in earnings per year on average at age 27. This study is here

4.1 Bivariate Random Variables and Distributions