(a) Using the sample mean values and the value of MSE, calculate the value of ?, the non-central parameter used for calculating power.

(b) Estimate the power of a test where ? = 0.01.

(c) Estimate the effect size, ?/?, using the sample values and MSE.

(d) If we wanted to have a power of 0.95 using an ? of 0.10, what sample size would we need in each group (at least)?

A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery and the time (in days) for successful completion of physical therapy. The fitness levels were measured as "Below Average" ( group I), "Average" (group II), or "Above Average" (group III). Summary statistics follow: I II III Overall Sample mean 38 32 24 32 Sample Std. Dev 5.48 3.46 4.43 6.88 Sample Size 8 10 6 24