This study presents a
statistical method for evaluating the effects of AMSP participation
on student learning. Measuring the effects of AMSP on student
achievement poses a research challenge because many factors influence
student test scores at a particular point in time. For example, a
student's math or science performance in the 8^{th} grade
is influenced by that student's learning in 7^{th} grade,
in 6^{th} grade and in all prior years. Furthermore, the
home environment of the student affects not only the performance of a
student as he or she enters pre-school but is known to influence the
gains of that student in future years. Characteristics of the school
such as its size also influence student gain scores. Building on the
premise of AMSP, the quality of the teacher should obviously also
influence the student's learning.

The above suggests that to measure the independent effect of the teacher and, in particular, the effects of AMSP participation by teachers on student outcomes, research models must account for other factors that are expected to affect student achievement or learning. It is not sufficient to examine levels of scores prior to the introduction of AMSP and compare those to scores after AMSP is in place as this ignores other factors that may be contributing to the change in scores.

The work to be presented consists of a description of a two stage model to estimate the independent effects of AMSP participation on student outcomes. A two stage model is used because beyond the challenges posed above, estimation is also complicated by the fact that teachers and schools voluntarily choose to participate in AMSP. The first stage of the model corrects for the nonrandom nature of selection of schools and teachers into AMSP which, uncorrected, also can bias the estimates of the program effects. The second stage then incorporates the first stage selection estimates and includes other independent variables that would be expected to influence test scores. This two-stage model allows us to interpret the estimated coefficients as the size of the effect of each variable on student math and science standardized test scores in Kentucky, independently of all other effects on test scores. Of course, the variable of greatest interest for our purpose is the one that measures the extent of participation in AMSP. Details on the model are presented (3.) below.