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Difficulty: HardHypothesis Testing and Statistical Power

A randomized controlled trial is evaluating a novel intensive lifestyle intervention against standard care for reducing fasting blood glucose in adults with prediabetes. The primary outcome is the mean change in fasting blood glucose after 6 months. Initial sample size calculations indicate that 300 participants are required to provide 80% statistical power to detect a 10 mg/dL difference between groups, using a two-sided α\alpha of 0.05 and an anticipated standard deviation (SD) of 20 mg/dL.

Prior to patient enrollment, the central laboratory transitions to a new, highly precise point-of-care assay. A pilot validation study confirms that this new assay reduces the anticipated SD of the fasting blood glucose measurements from 20 mg/dL to 10 mg/dL. The investigators decide to proceed with the originally planned sample size of 300 participants without altering the α\alpha level.

Assuming the true effect size remains 10 mg/dL, which of the following best describes the statistical impact of utilizing the new laboratory assay?

  1. A
    The primary outcome must now be analyzed using a Chi-square test rather than a Student's t-test.
  2. B
    The positive predictive value of a statistically significant finding will become independent of the pre-test probability of the intervention's efficacy.
  3. C
    The probability of committing a Type I (α\alpha) error will decrease because of the reduced measurement variability.
  4. The probability of committing a Type II (β\beta) error will decrease.Answer
  5. E
    The increased precision will allow researchers to interpret baseline demographic confounders as effect modifiers.

Answer

The probability of committing a Type II (β\beta) error will decrease.
The correct answer accurately states that the probability of a Type II error will decrease. Statistical power is the probability of correctly rejecting the null hypothesis when a true difference exists (Power = 1 - β\beta). Power is determined by the α\alpha level, sample size, effect size, and variance (standard deviation). Because the new assay reduces the standard deviation by half, the signal-to-noise ratio improves dramatically. With sample size and α\alpha held constant, this increases the statistical power. An increase in power mathematically dictates a corresponding decrease in β\beta, the probability of committing a Type II error.

Step-by-Step Solution

1
Identify the trial parameters being modified.
The standard deviation (SD) is decreasing from 20 mg/dL to 10 mg/dL, while sample size (N = 300), effect size (10 mg/dL), and alpha (0.05) remain constant.
To determine how statistical properties are affected, you must isolate the changed variable.
2
Relate the change in SD to statistical power.
A smaller SD reduces the standard error of the mean difference, thereby increasing the precision of the estimate and increasing the statistical power of the trial.
Statistical power is inversely proportional to variance; lower variance (SD) yields higher power.
3
Correlate statistical power to error types.
Power is defined as 1 - β\beta (where β\beta is the probability of a Type II error). Therefore, an increase in power mathematically guarantees a decrease in the probability of a Type II error.
To select the correct option describing the statistical impact.

Key Concept

Reducing the variance (standard deviation) of an outcome measure, while keeping sample size and effect size constant, increases statistical power and decreases the probability of a Type II error.
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Topics

Hypothesis Testing and Statistical Power

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