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Difficulty: EasyStatistical Inference and Hypothesis Testing

A research group evaluates a novel topical antibiotic for treating mild cellulitis in an outpatient setting. They randomly assign 60 patients to receive either the novel antibiotic or standard oral cephalexin. After completing the treatment course, the researchers find no statistically significant difference in cure rates between the two groups (p=0.22p = 0.22). They conclude that the novel topical agent is not superior to the standard oral therapy. However, a subsequent large-scale, multi-center randomized controlled trial involving 3,000 patients definitively establishes that the topical antibiotic actually has a significantly higher cure rate than cephalexin. Which of the following statistical concepts best explains the erroneous conclusion reached in the initial, smaller study?

  1. Type II errorAnswer
  2. B
    Type I error
  3. C
    Confounding
  4. D
    Effect modification
  5. E
    Recall bias

Answer

Type II error
The initial study concluded there was no significant difference between the two antibiotics, which means the researchers failed to reject the null hypothesis. However, the larger subsequent study revealed that a difference truly does exist, meaning the null hypothesis is actually false. Failing to detect a true difference is the exact definition of a Type II error (a false-negative result). This commonly occurs in studies with inadequate statistical power due to small sample sizes (such as n=60n = 60).

Step-by-Step Solution

1
Identify the conclusion of the initial study.
The initial study found no statistically significant difference (p=0.22p = 0.22) and failed to reject the null hypothesis.
Establishing the statistical outcome of the first study is necessary to determine what type of conclusion was made.
2
Determine the true state of reality based on the larger subsequent study.
The definitive large-scale trial showed that a significant difference truly exists (the null hypothesis is false).
Comparing the initial study's conclusion to the definitive reality reveals the nature of the statistical error.
3
Match the scenario to the definitions of statistical errors.
Failing to reject a false null hypothesis defines a Type II error.
Understanding standard definitions allows for the correct classification of the false-negative result.

Key Concept

A Type II error (represented by β\beta) occurs when a study fails to reject a false null hypothesis. In clinical terms, it means the study incorrectly concludes there is no difference or effect when one truly exists, often because the study had too small of a sample size and lacked adequate statistical power.
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Statistical Inference and Hypothesis Testing

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