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Zorluk: KolayHypothesis Testing and Statistical Power

A team of researchers is designing a randomized controlled trial to evaluate a new oral anticoagulant compared to warfarin for the prevention of stroke in patients with atrial fibrillation. The investigators determine that they need a sample size of 2,000 patients to have an 80% probability of detecting a 15% relative risk reduction in stroke incidence, assuming a significance level (α\alpha) of 0.05. Due to funding constraints, the researchers are forced to decrease their sample size to 1,000 patients while keeping the significance level and the expected effect size constant. Which of the following statistical metrics will most likely increase as a direct result of this modification?

  1. A
    The probability of committing a Type I error
  2. The probability of committing a Type II errorCevap
  3. C
    The statistical power of the study
  4. D
    The true effect size of the intervention
  5. E
    The positive predictive value of the study results

Cevap

The probability of committing a Type II error
Decreasing the sample size reduces the statistical power of a study. Statistical power (often represented as 1−β1 - \beta) is the probability of correctly rejecting a false null hypothesis. It is inversely related to the Type II error rate (β\beta), which is the probability of failing to detect a true difference. Therefore, a decrease in statistical power directly results in an increase in the probability of committing a Type II error.

Adım Adım Çözüm

1
Identify the primary change being made in the clinical trial design.
The sample size is being decreased from 2,000 to 1,000 patients.
Understanding the variable being manipulated is essential to predicting the statistical outcome.
2
Determine the relationship between sample size and statistical power.
A smaller sample size leads to a decrease in statistical power.
Statistical power relies on having enough data to confidently detect a true effect; fewer participants mean less confidence and lower power.
3
Relate the change in statistical power to the probability of committing statistical errors.
Statistical power is mathematically defined as 1−β1 - \beta, where β\beta is the probability of a Type II error.
Since power and Type II error probability are inversely related, a decrease in power directly results in an increase in the Type II error probability.

Anahtar Kavram

Decreasing the sample size of a clinical trial decreases its statistical power, which consequently increases the probability of committing a Type II error (β\beta).
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Konular

Hypothesis Testing and Statistical Power

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