The Elementary Teachers' Federation of Ontario make the following claim on their website as of February 13, 2013:

For years, the Elementary Teachers' Federation of Ontario (ETFO) has lobbied for small class sizes in the promary grades (Junior Kindergarten to Grade 3 inclusive). Class sizes in junior and intermediate classrooms have also been of signi?cant concern to teachers, but the government has been slow to implement perceptible imprvoements in these class sizes.

For its part, the Ontario Minsitry of Education reports that between the 2003-4 school year and the 2011-12 school year primary grade classes with 20 or fewer students increased as a percentage of the total from 31 percent to 91 percent. This change was realized by adding 2000 new primary grade classrooms and 5,000 additional teachers.

Still, the ETFO's position, as of February 14, 2013, is that not enough has been accomplished, that single grade classes should be no bigger than 15 students in Junior Kindergarten, 16 in Senior Kindergarten, and 18 in Grades 1 through 3. The Federation appears to rely for its evidence on a paper that reports some of the State of Tennessee's Student Teacher Achivement Ratio (STAR) study conducted over four years beginning in the1985 school year. Unfortunately, the link to the paper, produced by a private corporation, was removed when the company appears to have been dissolved.

A Brookings Institute paper by Chingos and Whitehurst characterizes the results of the STAR study as "the most in?uential and credible study of [classroom size reduction." The main research objective of the Tennessee study was to assess the importance of class size reductions as a way to improve student performance in the early grades. One subsidiary goal was to assess whether the potential  persistence of the effect of being in a small class carried over (persi in test results in subsequent year.

The research team chose the particularly powerful approach of randomly assigning teachers and about 6,300 kindergarten students to one of three types of classes:

(1) small classes with 13-17 students. (128 classes)
(2) Regular classes with 22-25 students. (101 classes)
(3) Regular classes with 22-25 students and a full-time aide. (99 classes)

The panel of students was initially tracked over the four primary grades, with measurements of their reading and arithmetic skills, based on standard tests taken at the end of each school year. They were subsequently tested in Grades 4 to 8. At the appropriate times, students' high school transcripts an college entrance examination results were added to the database.

Other factors that might explain some of the variation in student performance were also measured. These include measures of a teacher's professional experience, their highest educational credential (BA, MA, PhD), and a measure of the socioeconomic status of the student's family at the time they entered kindergarten. The full database is available on MyLearningSpace in Stata, star.dta, and "old Stata", star_old_Stata.dta, formats. The attached table provides a catalogue of the variables in the database.

Problem It is important to the success of an experiment like this one that assignment to each of the treatment levels be independent of any other variable that might affect student test results. If for example, teachers in the small classes happened to be more experienced than the teachers assigned to both types of regular classes, we would not be able to separate the effects of teacher experience and class size on student test performance. The problem arises becaause we suspect that students in much smaller classes are likely to perform better and students taught by more experienced teachers are likely to do better as well. That is the association between class size and teacher experience will amplify the difference in test scores between small and regular classes. See if you can justify the statement:

if less experienced teachers are more likely to be assigned to small classes, the relationship of class size with teacher experience will tend to attenuate differences in test score results.

I want you to the distributions of kindergarten teachers' experience by class- room type. Use Stata to report the summary statistics for the variable totexpk by cltypek. The latter is a categorical variable that indicates the type of class that a student was assigned to in kindergarten. The categories are identi?ed as follows: 1 (Small class), 2 (Regular), 3 (Regular with aide). Do you see anything that might raise some concern about identifying the effect of class size when you compare the distributions of experience by type of class?