A RCT comparing the efficacy of 2 drugs showed a difference between them (with a p-value < 0.05). Assume that in reality, however, the two drugs don't differ. This is?

Appeared in: AIIMS CRE SNO - 2023

Explanation

A Type 1 error occurs when a researcher incorrectly rejects a true null hypothesis.
This is also known as a 'false positive' or an alpha (α) error.
In the given scenario, the study found a significant difference (p < 0.05), leading to the rejection of the null hypothesis (the assumption of no difference).
However, the problem states that in reality, the drugs do not differ, meaning the null hypothesis was true.
Therefore, rejecting a true null hypothesis is the definition of a Type 1 error.

Option B: A Type 2 error is a 'false negative,' where a study fails to detect a real difference. The scenario describes finding a difference, not missing one.
Option C: Type 3 error is not a standard statistical term and refers to a different kind of mistake (e.g., getting the direction of the effect wrong). It does not fit the scenario of finding a difference that doesn't exist.
Option D: Type 4 error is not a standard, universally accepted term in biostatistics and is not relevant to this common hypothesis testing scenario.

Visual 1: 2x2 Table. A grid illustrating the four possible outcomes of hypothesis testing: True Positive (Correct), True Negative (Correct), Type 1 Error (False Positive), and Type 2 Error (False Negative). This visually clarifies the relationship between study results and reality.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Statistical Errors in Hypothesis Testing as background academic context rather than a clinical decision trigger.
Understanding statistical errors is crucial for evidence-based nursing practice. A Type 1 error can lead to the adoption of an ineffective or even harmful treatment, believing it to be superior.
This can result in negative patient outcomes, increased healthcare costs, and misdirection of future research efforts.
What if? If the p-value was 0.08 (not significant) but in reality, one drug was truly superior, this would be a Type 2 error. A potentially valuable treatment might be wrongly discarded, denying patients a beneficial therapy.

How to Approach the Question

First, identify the null hypothesis (H₀), which is the statement of no effect or no difference. Here, H₀ is 'The two drugs do not differ in efficacy.'
Next, determine the study's conclusion based on the p-value. A p-value < 0.05 means the result is statistically significant, so the study rejects the null hypothesis.
Then, identify the 'reality' as stated in the question. Here, 'in reality... the two drugs don't differ,' which means the null hypothesis is actually true.
Finally, match the situation to the correct definition. The study rejected a null hypothesis that was, in reality, true. This is the textbook definition of a Type 1 error.

Concept Tested & Keywords

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