Question

Rehabilitation therapy. A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful rehabilitation. Patient records in the rehabilitation center were examined, and 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) for each patient follow:

Table 1: Data for problem 16.9

	i	1	2	3	4	5	6	7	8	9
1	below average	29	42	38	40	43	40	30	42
2	average	30	35	39	28	31	31	29	35	29	33
3	above average	26	32	21	20	23	22

Assume that ANOVA cell mean model (16.2) is appropriate:

(a) Do the factor level means appear to differ? Does the variability of the observations within each factor level appear to be approximately the same for all factor levels?

(b) Obtain the fitted values.

(c) Obtain the ANOVA table

Answer 1

(a) Do the factor level means appear to differ? Does the variability of the observations within each factor level appear to be approximately the same for all factor levels?

The factor level appears to be different. The variability of the observations within each factor level appears to be approximately the same for all factor levels.

(b) Obtain the fitted values.

y = 192 + 16*x1 + 14.2*x2 + 19.8*x3

(c) Obtain the ANOVA table

Source	SS	df	MS	F	p-value
Treatment	672.00	2	336.000	16.96	0.0000
Error	416.00	21	19.810
Total	1,088.00	23