The study described in Exercise R5.21 also looked at scores in mathematics and language. Here are software outputs for the appropriate tests.

 

Data From Exercise R5.21

Several programs attempt to address  the shortage of qualified teachers by placing uncertified instructors in schools with acute needs—often in inner cities. A study compared students taught by certified teachers to others taught by uncertified teachers in the same schools. Reading scores of the students of certified teachers averaged 35.62 points with standard deviation 9.31. The scores of students instructed by uncertified teachers had mean 32.48 points with standard deviation 9.43 points on the same test. There  were 44 students in each group. The appropriate t-procedure  has 86 degrees of freedom. Is there evidence of lower scores with uncertified teachers? Discuss. (The Effectiveness of “Teach for America” and Other Under-certified Teachers on Student Academic Achievement: A Case of Harmful Public Policy. Education Policy Analysis Archives)