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Difficulty: MediumHypothesis Testing and Statistical Power

A hospital infection control committee is evaluating a new ultraviolet (UV) room disinfection protocol to reduce the incidence of hospital-acquired *Clostridioides difficile* infections. A crossover trial is conducted across four medical wards. Because the new protocol requires significant capital investment and additional staffing, the hospital administration insists on highly rigorous evidence before adopting the technology hospital-wide. To ensure this, the investigators set the predetermined significance level (α\alpha) at 0.010.01 rather than the conventional 0.050.05. The overall duration of the study and the total number of patient admissions monitored will remain exactly as originally planned. Which of the following is the most likely statistical consequence of applying this more stringent significance threshold?

  1. Increased probability of failing to identify a true reduction in infection ratesAnswer
  2. B
    Increased probability of falsely concluding that the protocol reduces infection rates
  3. C
    Increased statistical power to detect a small difference in infection rates
  4. D
    Increased independence of the study's negative predictive value from the baseline prevalence of infection
  5. E
    Reduced susceptibility of the study results to unrecognized effect modification

Answer

Setting a more stringent significance level (α=0.01\alpha = 0.01) decreases statistical power, which corresponds to an increased probability of committing a Type II error (failing to identify a true reduction in infection rates).
The significance level (α\alpha) represents the probability of committing a Type I error, which is rejecting a true null hypothesis. By lowering α\alpha from 0.050.05 to 0.010.01, the investigators make the criteria for statistical significance more stringent, thereby reducing the risk of a false-positive conclusion. However, α\alpha and β\beta (the probability of a Type II error) are inversely related when the sample size is fixed. A Type II error occurs when a study fails to reject a false null hypothesis (a false negative). Therefore, decreasing α\alpha inevitably increases β\beta, which directly translates to an increased probability of failing to identify a true reduction in infection rates. Because statistical power is defined as 1−β1 - \beta, the overall power of the study decreases.

Step-by-Step Solution

1
Identify the proposed methodological change in the trial design.
The significance threshold (α\alpha) is tightened from 0.050.05 to 0.010.01 while maintaining the same fixed sample size and study duration.
To isolate which statistical parameters are directly affected by this specific adjustment.
2
Analyze the direct relationship between α\alpha and Type I error.
A lower α\alpha directly reduces the probability of committing a Type I error (a false positive conclusion).
The α\alpha level explicitly defines the maximum acceptable Type I error rate established before the study begins.
3
Determine the downstream effect on Type II error (β\beta) and statistical power.
Because α\alpha and β\beta are inversely related for a fixed sample size, lowering α\alpha inevitably increases β\beta.
Shifting the critical value to be more stringent makes it mathematically harder to reject the null hypothesis, thereby increasing the chance of missing a true clinical effect (a Type II error).

Key Concept

In a study with a fixed sample size, there is an inverse relationship between the probability of a Type I error (α\alpha) and a Type II error (β\beta). Decreasing α\alpha increases β\beta, which consequently decreases the statistical power (1−β1 - \beta) of the study.
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Topics

Hypothesis Testing and Statistical Power

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