In a study of the palatability of antibiotics in children, Dr. Doreen Matsui and colleagues used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics.5 The children's response was measured on a 10-centimeter (cm) visual analog scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data (simulated from the results of Matsui's report), each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analog scale from 0 to 10 cm.

a. What design is used in collecting these data?
b. Using an appropriate statistical package for a two way classification, produce a normal probability plot of the residuals as well as a plot of residuals versus antibiotics. Do the usual analysis of variance assumptions appear to be satisfied?
c. Use the appropriate nonparametric test to test for differences in the distributions of responses to the tastes of the four antibiotics.
d. Comment on the results of the analysis of variance in part b compared with the nonparametric test in part c.

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