Here is a case study worksheet that I developed to walk some graduate students in the health sciences (not stat/biostat majors) through the basics of power and sample size calculations using JMP software. The idea was to tackle a research problem from a few different angles to give them an idea of simple sample size calculations in practice. The worksheet was well received and student feedback indicated that they did not realize how much consideration of previous work and relating data collection to research hypotheses was needed in general practice.
I admit that any of these questions could use better phrasing and feedback is certainly welcome.
Power Worksheet - JMP
Suppose that we decide to do a design of a new physical activity program designed specifically to target obese teens in a semi-rural setting. What we need to know before designing this program is how much exercise at risk teens get? So we want to use some preliminary studies to show the need for such a program in this area. Troiano et al (Medicine & Science in Sports & Exercise 2008) estimates the combined number of minutes per day spent in moderate to vigorous physical activity (PA). For males aged 16-19 the estimated mean minutes is 32.7(standard deviation 35.27) and for females 16-19 the estimated mean minutes is 19.6 (standard deviation 37.64). Among the 16-19 cohorts there were 257 males and 246 females.
Answer the questions below; the power applet in JMP software will be useful for some questions. Assume a level of significance of 0.05 for all hypothesis tests and sample size calculations should be done with 80% power.
Use an independent samples t-test to determine if there is a statistically significant difference between the male and female groups in terms of mean combined moderate to vigorous physical activity per day.
Let’s suppose that I wanted to show that obese teens (BMI > 95 percentile) have a mean combined minutes of physical activity that is half of the general population (so about 16.35 min per day boys and 9.8 minutes per day for girls). Assuming that the standard deviations are the same as above how many boys and girls do I need to recruit in separate studies for such an outcome? Assume that the non-obese population is the same as the general population for each cohort.
How many males do you need in each of the obese and non-obese groups? (hint: the mean in the non-obese group is 32.7 and the mean in the obese group is 16.5 and assume a common standard deviation of 35.27)
How many females do you need in each of the obese and non-obese groups?
Suppose that my assumptions are wrong and I won’t be able to show that the obese teens have half the activity of the non-obese teens. Do a power curve for the difference between the two groups for each gender (one for males and one for females) with difference on the x-axis and power on the y-axis. Here we will assume the standard deviations are as before but assume that we can recruit 100 people per group.
It is recommended that teens get at least 60 minutes of physical activity per day. Instead of working with means and standard deviations, let’s frame our hypotheses in terms of proportions. Suppose we believe that 20% of non-obese males 16-19 get at least 60 minutes of PA per day, while only 10% of obese teens get 60 minutes of PA per day. What sample size would we need to demonstrate the hypothesized result? Study considerations here are irrespective of gender.
Let’s say we do some of the above research and show the differences we have described above. Suppose under a proposed new exercise regimen the obese teens go from 20 minutes of PA per day to 45 minutes of activity per day. The researcher wants one his/her graduate assistants to study this regimen in an overweight group of males (suppose recruited to be 200 lbs + and BMI > 95 %). They believe the standard deviation of weights in this group will be 15 lbs both before and after one month on this program. If I recruit 25 volunteers, how much weight will they have to lose in order to show a statistically significant difference with power 0.80 and significance level 0.05?