A study determines that the mean blood cholesterol level is 195 mg/dL in 200 non-diabetic hospitalized patients and 210 mg/dL in 180 diabetic hospitalized patients. The probability that the observed difference is due to chance alone is reported to be 5%. There is also a 20% probability of concluding that there is no difference in blood cholesterol level when there is one in reality. What is the power of the study?

Question

A study determines that the mean blood cholesterol level is 195 mg/dL in 200 non-diabetic hospitalized patients and 210 mg/dL in 180 diabetic hospitalized patients.  The probability that the observed difference is due to chance alone is reported to be 5%.  There is also a 20% probability of concluding that there is no difference in blood cholesterol level when there is one in reality.  What is the power of the study?

Quizplus · Accepted Answer

The power of a study is the ability of a study to detect a difference between groups when such a difference truly exists. Power is related to type II error (β), which is the probability of concluding there is no difference between groups when one truly exists. Mathematically, power is given by: In this example, the power of the study is the probability of detecting a difference in blood cholesterol level between diabetics and non-diabetics if there is a real difference. The probability of concluding that there is no difference in blood cholesterol level when in reality there is one is given as 20%; this corresponds to the definition of β (ie, β = 0.20 in this example). Therefore: (Choice A) Type I error (α) describes the probability of seeing a difference when there is no difference in reality. The value of α is generally compared to the probability that the observed difference is due to chance alone (a simplified explanation of the p-value). In this example, the probability that the observed difference between diabetic and nondiabetic patients is due to chance alone is given as 5% (0.05). (Choices B and E) Type II error (β) is 0.20, as explained above. The value 0.95 corresponds to (1 - α), but power is given by (1 - β). Educational objective: The power of a study indicates the probability of seeing a difference when there is one. The formula is Power = 1 - β, where β is the type II error rate.

A Study Determines That the Mean Blood Cholesterol Level Is