In a randomized trial comparing the efficacy of two antidiabetic drugs, no significant difference was found between the two drugs. However, in reality, there was a significant difference in the two drugs. This is an example of?

1. A

   β error

2. B

   α error

3. C

   1α

4. D

   2β

Appeared in: NORCET 5 mains

Explanation

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• A β (beta) error, also known as a Type II error, occurs when a study fails to reject a false null hypothesis.
• In this scenario, the null hypothesis (H₀) is that there is no difference between the two antidiabetic drugs.
• The study's conclusion was 'no significant difference,' meaning it failed to reject the null hypothesis.
• However, in reality, a 'significant difference' did exist, which means the null hypothesis was false.
• This situation, where a study misses a real effect and concludes there is no difference, is defined as a Type II error or a 'false negative'.

Why Other Options Were Wrong

• Option B: An α (alpha) error, or Type I error, is the opposite. It occurs when a study concludes there IS a significant difference, but in reality, there is NOT. This is a 'false positive'.
• Option C: 1-α is not a type of error. It represents the confidence level of a statistical test. For example, if the significance level (α) is 0.05 (or 5%), the confidence level (1-α) is 0.95 (or 95%).
• Option D: 2β is not a standard term in statistics. The probability of a Type II error is simply denoted by β (beta).

Related Visual

• Visual 1: Diagram - A 2x2 grid illustrating the four possible outcomes of hypothesis testing. The grid's axes would be 'Study Conclusion' (Reject H₀ vs. Fail to Reject H₀) and 'Reality' (H₀ is True vs. H₀ is False). The four cells would be labeled: Correct Decision (True Negative), Type I Error (False Positive), Type II Error (False Negative), and Correct Decision (True Positive/Power).

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 (Type I vs. Type II error) as background academic context rather than a clinical decision trigger.
• Nurses must critically appraise research to ensure evidence-based practice. Understanding Type I and II errors is fundamental to judging the validity and applicability of study findings.
• A Type II error in a clinical trial can lead to the premature abandonment of a new, potentially effective treatment, thus denying patients a beneficial therapy.
• What if the study had a very small sample size? A small sample size decreases the statistical power of a study, which significantly increases the risk of committing a Type II error. The study may not have enough participants to detect a true, but subtle, difference between the drugs.

How to Approach the Question

• First, identify the null hypothesis (H₀) of the study. In this case, H₀ is: 'There is no significant difference between the two antidiabetic drugs.'
• Next, identify the conclusion of the study. The study found 'no significant difference,' which means it failed to reject the null hypothesis.
• Then, identify what the 'reality' was. In reality, 'there was a significant difference,' which means the null hypothesis was false.
• Finally, match the situation to the correct definition. The study failed to reject a false null hypothesis.
• Recall the definitions: Failing to reject a false null hypothesis is a Type II error (β error). Rejecting a true null hypothesis is a Type I error (α error).

Concept Tested & Keywords

• Concept Tested: Statistical errors in hypothesis testing (Type I vs. Type II error)
• Stem keywords: randomized trial, antidiabetic drugs, no significant difference, reality, significant difference
• Lead-in keywords: example of

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