Sample size table for Student's independent t-test where p = .05, two-tailed.

Effect Size Power .40 .50 .60 .70 .80

.70 78 50 35 26 20

.75 88 57 40 29 23

.80 99 64 45 33 26

.85 113 73 51 38 29

.90 132 85 59 44 34

.95 163 105 73 54 42

.99 231 148 103 76 58

Etanercept is an drug that blocks tumor necrosis factor alpha and is used for treating rheumatoid arthritis. Assume that clinical researchers have reason to believe that giving patients Etanercept plus methotrexate will be a more effective treatment. Going to a clinical database, investigators identify a group of patients who have rheumatoid arthritis and who have been given Etanercept only. They specifically look at the number of swollen joints that are recorded for each patient and determine that the mean and standard deviation are 5.81 and 4.75, respectively. They believe that adding methotrexate should improve (i.e., reduce) the swollen joint count by 30%. The investigators plan to conduct a randomized clinical study in which they will have two groups of patients. One group will get Etanercept only and the other will get Etanercept + methotrexate. They plan to use 50 subjects per group. The dependent variable will be swollen joint count. The investigators plan to test the impact of the combined drug regimen with a two-tailed Student's t-test for independent samples and want to establish statistical significance at the .05 level.

1) Using the information that was obtained from the clinical database, compute the effect size that the investigators anticipate with the combined drug regimen.

Here is the link to conduct the calculations for Tasks 2 and 3: https://www.stat.ubc.ca/~rollin/stats/ssize/n2.html

2) If the investigators proceed with 50 patients per group, what will be the power for detecting the above effect size?

3) If the investigators want to conduct a study that will provide an 80% chance of detecting the above effect size (i.e., 80% power), how many patients do they need per group?