In a 5-year follow-up of bilateral stimulation of the subthalamic nucleus among 49 patients with advanced Parkinson’s disease, investigators assessed changes in symptoms as measured by the Unified Parkinson’s Disease Rating Scale (range= 0 to 108, with higher values denoting more symptoms). Assume this measure follows a normal distribution. The mean score at baseline was 55.7. The standard deviation of change from baseline to 5 years was 15.3. 

What minimum sample size would be needed to detect a mean change of 5 units with 80% power if a two-sided test is used with alpha=0.05?

In a 5-year follow-up of bilateral stimulation of the subthalamic nucleus among 49 patients with advanced Parkinson’s disease, investigators assessed changes in symptoms as measured by the Unified Parkinson’s Disease Rating Scale (range= 0 to 108, with higher values denoting more symptoms). Assume this measure follows a normal distribution. The mean score at baseline was 55.7. The standard deviation of change from baseline to 5 years was 15.3. 

The above study had no control group. Assuming that the same standard deviation of change would occur among controls and the mean change among controls=0, how many participants would be necessary to detect a mean difference of 5 units of change between those receiving stimulation and a control group of equal size with 80% power if a two-sided test is used with apha=0.05?

In a 5-year follow-up of bilateral stimulation of the subthalamic nucleus among 49 patients with advanced Parkinson’s disease, investigators assessed changes in symptoms as measured by the Unified Parkinson’s Disease Rating Scale (range= 0 to 108, with higher values denoting more symptoms). Assume this measure follows a normal distribution. The mean score at baseline was 55.7. The standard deviation of change from baseline to 5 years was 15.3. 

How much power does this study have to detect a mean difference of 5 units in the symptom scale if a two-sided test is used with alpha=0.05?