A new drug designed to control neuropathic pain needs to be tested using pain score measurements (on a scale of 0 - 10; 0 = no pain). Clinicians think that a standard deviation of 2 for the pain score would be a suitable value. For the drug to be carried forward a minimum decrease in the pain score of 1 is needed.

(a) Suppose that the trial is designed to have 90% power to find a minimum treatment effect of 1 at a 5% significance level. What would be a suitable sample size?

(b) Suppose that the power is changed to 80%, what is a suitable sample size now?

(c) Suppose that the trial only recruited 300 patients, what would be the minimal treatment difference that could be detected with 80% power?

(d) What if the minimal treatment difference is changed to 2 (but the power remains at 80%), and that we want the patients allocated to the two arms in the ratio 2:1. What would be an appropriate sample size?

Additional Information

This kinds of question lies from Statistics and it is about a proposed study for a new drug controlling neuropathic pain. A scale of measurement for pain management has been taken and to know if the drug works, the scale must come down by at least 1 point. The solution discusses the various questions about this study.