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Difficulty: EasyStatistical Inference and Hypothesis Testing

Investigators are designing a clinical trial to evaluate a novel monoclonal antibody for the treatment of severe asthma. During the study design phase, they establish an acceptable probability of a Type I error (α\alpha) at 0.050.05. They also calculate that the probability of failing to reject the null hypothesis when it is actually false is 0.200.20. What is the statistical power of this study expressed as a percentage?

Answer: 80 %

Answer

80
The statistical power of a study is defined as the probability of correctly rejecting the null hypothesis when it is indeed false. It is mathematically defined as 1−β1 - \beta, where β\beta is the probability of making a Type II error. In this scenario, the probability of failing to reject a false null hypothesis (Type II error) is 0.200.20. Therefore, the power is 1−0.20=0.801 - 0.20 = 0.80, which corresponds to 80%80\%.

Step-by-Step Solution

1
Identify the provided variables from the vignette.
The probability of a Type I error (α\alpha) is 0.050.05, and the probability of a Type II error (β\beta) is 0.200.20.
Recognizing the definitions of alpha and beta errors is necessary to select the correct formula for power.
2
Recall the formula for statistical power.
Power = 1−β1 - \beta
Statistical power is defined as the probability of correctly rejecting a false null hypothesis, which is the complement of the Type II error rate.
3
Calculate the power and convert it to a percentage.
Power = 1−0.20=0.801 - 0.20 = 0.80, which is 80%80\%.
The question specifically asks for the power expressed as a percentage.

Key Concept

Statistical power is the probability of correctly rejecting the null hypothesis when it is false. It is calculated as 1−β1 - \beta, where β\beta is the Type II error rate.
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Topics

Statistical Inference and Hypothesis Testing

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