6. le Riche and Csima (1964) evaluated four hypnotic drugs and a placebo to determine their eect on quality of sleep in elderly patients. The treat-

ment levels were labeled (A=Placebo, B=Ethchlorvynol, C=Glutethimide, D=Chloral hydrate and E=Secobarbitol sodium). Elderly patients were given one of the capsules for ve nights in succession and their quality of sleep was rated by a trained nurse on a four-point scale (0=poor to 3=excel-

lent) each night. An average score was calculated for each patient over the ve nights in a week. Each patient received all ve treatments in successive weeks. A Latin-square design was used to account for patient-to-patient dierences and week-to-week eects. The design and the response (mean quality of sleep rating) are shown in the table on the next page.

(a) What is the appropriate model for this data?

(b) Complete the ANOVA and determine if there are any signicant dier-

ences among the treatments.

(c) Use an appropriate method to determine if there is a signicant dierence between the placebo and the average of the other drugs, and if there are signicant dierences among the four drugs.

(d) Use residual plots to check the assumptions for the model you t.

Transcribed Image Text:

Patient 1 2 Week 3 4 5 1 B (2.92) E (2.43) A (2.19) C (2.71) D (2.71) 2 D (2.86) A (1.64) E (3.02) B (3.03) C (3.03) 3 E (1.97) B (2.50) C (2.47) D (2.65) A (1.89) 4 A (1.99) C (2.39) D (2.37) E (2.33) B (2.71) 5 C (2.64) D (2.31) B (2.44) A (1.89) E (2.78)