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Difficulty: MediumHypothesis Testing and Statistical Power

A clinical research committee is reviewing a series of proposals for upcoming therapeutic trials. As part of the methodological review, the biostatistician evaluates how specific study design modifications will impact error rates and statistical power. Match each proposed trial modification with its primary statistical consequence.

  • Decreasing the significance level (α\alpha) from 0.050.05 to 0.010.01Reduces the probability of falsely rejecting a true null hypothesis, but consequently increases the β\beta error rate.
  • Increasing the total sample size (nn) of the trial cohortNarrows the standard error of the mean, thereby increasing the probability of correctly identifying a true difference.
  • Discovering the true clinical effect size is smaller than initially estimatedCauses the alternative hypothesis curve to shift closer to the null, resulting in decreased statistical power.
  • Implementing strict inclusion criteria that significantly decrease population varianceIncreases power by reducing the overall spread of the data, though this may limit the generalizability of the findings.

Answer

Decreasing α\alpha matches with reducing false rejections but increasing β\beta error. Increasing sample size matches with narrowing standard error. A smaller effect size matches with shifting the alternative curve closer to the null. Decreasing variance matches with reducing data spread and increasing power at the cost of generalizability.
Each modification predictably alters the statistical mechanics of a clinical trial. Lowering α\alpha decreases Type I errors but increases Type II errors. Increasing sample size reduces standard error, boosting statistical power. A smaller effect size brings the null and alternative distributions closer, dropping power. Reducing variance narrows the distributions, increasing power but limiting external validity.

Step-by-Step Solution

1
Analyze the impact of lowering the alpha threshold.
Matches with decreased Type I error and increased Type II (β\beta) error.
Alpha represents the Type I error rate; lowering it requires stronger statistical evidence to reject the null, making it more likely to miss a true difference.
2
Analyze the impact of increasing sample size (nn).
Matches with decreased standard error and increased power.
Standard error is inversely proportional to the square root of nn. A larger nn narrows the distributions, making differences easier to detect.
3
Analyze the impact of a smaller true effect size.
Matches with curves shifting closer together and decreased power.
Effect size is the actual difference between groups. A smaller difference means more overlap between the null and alternative distributions, increasing Type II error.
4
Analyze the impact of decreasing population variance.
Matches with reduced data spread and increased power.
Less variance means narrower curves and less overlap, which improves the ability to detect a difference, though highly restricted cohorts may not represent the general population.

Key Concept

The interconnected relationships between alpha, beta, statistical power, sample size, effect size, and variance in hypothesis testing.
Estimated Time:1m 30s
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Topics

Hypothesis Testing and Statistical Power

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