Question

You are the director of a diabetes clinic that has recently completed a pilot for a new disease management program intended to reduce blood glucose levels in the participants. In developing the pilot study, you set out to demonstrate that the program will be effective in reducing average blood glucose levels for the program’s participants. You hope to demonstrate the value of the program to your CEO by presenting the findings from a hypothesis test based on the results from the pilot study. After extensive preparation, including a comprehensive review of the literature and discussions with subject matter experts, the specifics of the disease management program were devised. The program consisted of individual counseling and education regarding lifestyle changes and healthy eating choices. The program recruited 50 patients who were seen twice a month, at which time they received individual counseling, along with having their blood sugars checked and tracked. The pilot lasted six months and required a fairly large resource commitment on the part of the clinic. Prior to beginning the program, participants had their blood glucose level drawn. The expectation was that the average blood glucose level of the group at the end of the pilot period would be lower than the average blood glucose level at the beginning of the pilot.

Over the course of the six-month pilot period, the program went well. The participants were engaged and seemed motivated, with very few missed appointments and no dropouts along the way. While the program ran smoothly the cost of the program compared to its value would continue to be a factor in whether the program would be renewed. The clinic expressed its commitment to continue the program if the program was found to be successful in reducing participants’ blood glucose levels. You are asked to prepare a report to the clinic’s CEO detailing the value of the disease management intervention. In collecting your data, you found that at the beginning of the pilot the group’s average blood glucose level was 257.5 milligrams per deciliter. At the end of the pilot period, the average blood glucose level for the group was 240 milligrams per deciliter. You have some knowledge of statistics and want to be pretty conservative in your analysis, so you set your desired alpha level at 0.01. You asked a statistician friend to run the numbers and she reported back with the following statistics:

Critical value: 2.412

t-value: -3.68

p-value: <0.01

Prepare a brief report to Dr. Wilhelmina Smith, CEO of the diabetes clinic, detailing your findings and your recommendation regarding whether the disease management program should be continued. In other words, you need to answer the question: Did the disease management program work? Your brief should, at a minimum, include the following details:

1. Present each step for hypothesis testing as described in the NEDARC resource Hypothesis Testing:
   1. State the alternative hypothesis (H_a) and null hypothesis (H_o) for your analysis. You will need to construct these for your report based on the scenario described above.
   2. Set the alpha level and explain its significance.
   3. Interpret the probability of H_o being true using the statistical results above.
   4. Explain whether the data supports accepting or rejecting the H_o.
2. Discuss the potential sources of errors (Type I and Type II) possible in all hypothesis testing exercises and provide an explanation of the practical ramifications to your decision of making an error of each type.
3. Provide your recommendation about whether to continue the program and a justification for your decision based on the results.

Answer 1