This lab has three major components. We will use S-Plus to:
Also look up the following two papers (electronic access through Duke's Library) and read:
Goodman, Steven N.and Berlin, Jesse A. 1994. The Use of Predicted Confidence Intervals When Planning Experiments and the Misuse of Power when Inerpreting Results. Annals of Internal Medicine. Vol 121 p 200-206; correction Annals of Internal Medicine Vol 122 p 478.
Moher, David, Dulerg, Corinne S., and Wells, George A. 1994. Statistical Power, Sample Size, and their Reporting in Randomized Controlled Trials. Journal of the American Medical Asociation. Vol 272 pp 122-124.
Read in the dataset boneden.xls
Twin 2 is the heavier smoking of the two twins in each case. Following the Case Study (page 38, page184-185, and page 260-261), Bone Mineral Density difference is determined by taking the value of the heavier smoking twin and subtracting the value of the lighter smoking twin, and then dividing the difference by the average of the twins, so that the BMD fo the femoral neck is defined as
BMDneck = (fn2 - fn1)/(.5*(fn1 + fn2))
Using the above expression, create a new column for BMDneck.
Use any appropriate graphical methods to check whether assumptions for testing or confidence intervals are OK. What do the graphical summaries suggest about the hypothesis?
Formally test whether there are significant differences in BMD in the femoral neck between the heavier and lighter smoking twins. What is the Null Hypothesis? What is the Alternative Hypothesis? (Is it two sided or one sided?) To perform the test in S-Plus, go to the Statistics menu and select Compare Samples and then choose One Sample, and then t Test... Select BMDneck for the Variable field. Fill in the Mean Under the Null Hypothesis and specify whether the Alternative Hypothesis is two-sided, or one-sided (is the mean under the alternative greater than the mean under the null or less than the mean unde the null?). Click on OK; the results will appear in the report window.
Based on your findings what type of health recommendations would you make? Turn in a consise one paragraph report summarizing your findings. You may include one figure. Your total report must be typed and fit on one page.
Sample size and power calculations are an important part of designing a study. If the sample size is inadequate for detecting a treatment effect with a certain level of probability, then the study may be a complete waste of time right from the start!
Work Exercises 7.32 and 7.33 by hand. The answers are in the back of the book. Now let's do the calculations in S-Plus. Go to the Statistics menu and select Power and Sample Size, then choose Normal Mean...
For both power and sample size we need to specify the standard deviation, the mean under the null and the mean under the alternative that we would like to be able to detect. Using the past data, enter these values in the appropriate fields (Standard deviation = 9, mean under the null = 0 , mean under the alternative = -4.8) . Use a two-sided test.
For Sample Size determination, enter the values for Alpha (0.05) and Power (0.90). Click on OK. Do your results agree with what you found by hand?
For Power, click on the Power button. Specify the Sample Sizes N1 (20), and fill in the standard deviations and means as before. Click on OK. Would designing a study with only 20 individuals be ethical in this case?
Write a short paragraph in the form of a methods section of a research paper that describes your sample size and power calculations.