Radial keratotomy is a type of refractive surgery in which radial incisions are made in a myopic (nearsighted) patient's cornea to reduce the person's myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, thereby reducing the patient's refractive error.
The incisions extend radially from the periphery toward the center of the cornea. A circular central portion of the cornea, known as the clear zone, remains uncut. The diameter of the clear zone is determined by the baseline refraction of the patient. Patients with a greater degree of myopia may receive longer incisions, leaving them with smaller clear zones. The thinking here is that "more surgery" is needed to correct the worse initial vision of these patients.
Radial keratotomy and other vision-correction surgery techniques grew in popularity in the 1980s and 1990s, both among the public and among ophthalmologists. The Prospective Evaluation of Radial Keratotomy (PERK) study was begun in 1983 to evaluate the effects of radial keratotomy. Lynn et al. (1987) examined the variables associated with the five-year postsurgical change in refractive error (Y, measured in diopters, D). One of the independent variables under consideration was diameter of the clear zone (X). In the PERK study, three clear zone sizes were used: 3.0 mm, 3.5 mm, and 4.0 mm.
The above computer output is based on data adapted from the PERK study.
a. Suppose that an ANOVA is to be performed to compare the average five-year change in refraction for patients with different clear zones. State precisely the ANOVA model. Is clear zone size a fixed- or random-effects factor?
b. In the above SAS output, complete the ANOVA table.
c. Test whether the average five-year change in refraction differs significantly by clear zone size. Interpret your results.
d. Use the Tukey-Kramer method to locate any significant pairwise differences between clear zones. (Use α = .05.) Interpret your results.