Question

Steady-state hemoglobin levels were measured on a total of N = 41 patients with k = 3 types of sickle cell disease. The k = 3 types are HB SS, HB ST (HB S/-thalassemia), and HB SC. The resulting data are displayed in Table 12.3.

SS	7.2	7.7	8.0	8.1	8.3	8.4	8.4	8.5	8.6	8.7	9.1	9.1	9.1	9.8	10.1	10.3
ST	8.1	9.2	10.0	10.4	10.6	10.9	11.1	11.9	12.0	12.1
SC	10.7	11.3	11.5	11.6	11.7	11.8	12.0	12.1	12.3	12.6	12.6	13.3	13.3	13.8	13.9

a. Use side-by-side boxplots and normal probability plots to investigate the ANOVA assumptions of normality and homoscedasticity. Do these assumptions seem plausible? Why or why not? b. Use ANOVA to test the null hypothesis that the three types of sickle cell disease have the same mean hemoglobin levels. Use a significance level of ? = 0.05 and organize your calculations in an ANOVA table. Note: For this problem, please calculate/compute all information (such as Sum of Squares, Mean Squares, Test Statistic and P-value) you need for the ANOVA table before checking with the “ANOVA” function in R. Please include appropriate labels in your plots!

Answer 1

(a)

Normality assumption is valid since the p-value for each group is large i.e. >0.05. However, three groups are not homoscedastic since the box plots corresponding to the three groups (SS, ST, and SC) are not equal in width.

(b)

One-way ANOVA: Response versus Group

Source DF SS MS F P
Group 2 99.8893 49.9447 49.9997 0.0000
Error 38 37.9585 0.9989
Total 40 137.8478

Since p-value=0.0000<0.05 hence we reject the null hypothesis that the three types of sickle cell disease have the same mean hemoglobin levels and conclude that there is at least one type is different from the other two.