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Difficulty: EasyHypothesis Testing and Statistical Power

A medical center conducts a randomized controlled trial comparing a newly developed lipid-lowering medication to a standard statin therapy in 150 patients with familial hypercholesterolemia. After six months, the investigators report that the new medication reduces low-density lipoprotein (LDL) cholesterol significantly more than the standard therapy (p=0.04p = 0.04). Based on these results, the medication is approved and widely prescribed at the institution. Two years later, a well-powered, multi-center trial with 5,000 patients reveals no statistically significant difference in LDL reduction between the two treatments. Assuming the large-scale trial's conclusion represents the true relationship, which of the following best describes the statistical phenomenon that most likely occurred in the initial study?

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

Answer

Type I error
The correct answer is Type I error, which occurs when a study incorrectly rejects a true null hypothesis. In hypothesis testing, this is considered a 'false positive.' In this scenario, the initial study found a statistically significant difference (p=0.04p = 0.04) when, in reality, there was no true difference between the treatments (as demonstrated by the definitive 5,000-patient trial). Claiming an effect exists when it actually does not is the classic definition of a Type I error.

Step-by-Step Solution

1
Identify the null hypothesis and the conclusion of the initial study.
The null hypothesis is that there is no difference between the new medication and the standard statin. The initial study rejected this null hypothesis (p=0.04p = 0.04).
Understanding the baseline statistical assumption is necessary to evaluate the type of error made.
2
Determine the 'true' relationship based on the scenario.
The definitive, well-powered large-scale trial showed no significant difference, indicating that the null hypothesis is actually true in reality.
Comparing the initial study's conclusion to the true population reality reveals the error.
3
Classify the discrepancy between the study's conclusion and reality.
The initial study claimed a difference existed when there was none. This is a false positive.
Classifying the error conceptually allows matching it to formal statistical terminology.
4
Match the false-positive finding to the correct statistical term.
A false positive in hypothesis testing is defined as a Type I error (denoted by α\alpha).
This directly answers the prompt's question.

Key Concept

A Type I error (false positive) occurs when a statistical test incorrectly rejects a true null hypothesis, often due to chance in an underpowered or small sample.
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Topics

Hypothesis Testing and Statistical Power

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