Question

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.

		j
	i	1	2	3	4	5	6	7	8	9	10
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

1. Explore the with side-by-side box-plots. Discuss the results of your graphical exploration.
2. Calculate group mean and standard deviation.
3. Complete a one-way analysis of variance for this problem. Show all hypothesis-testing steps and interpret the results.

Answer 1

Using Minitab:

a.

The boxplot for the data shows that Below Average has both the highest median and variability

Average and above average  appear to have roughly similar variability.

Part b.

Part c.

The p-value for the paint hardness ANOVA is 0.000. Thus, assuming you chose the commonly used a-level of 0.05 for the test, you would conclude that there are significant differences in physical therapy and the prior physical fitness status.