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Difficulty: MediumInferential Statistical Tests

A sleep medicine physician conducts a crossover study to evaluate the efficacy of a novel non-benzodiazepine hypnotic agent compared to placebo in patients with chronic insomnia. Twenty patients are enrolled. Each patient receives the placebo for one week, undergoes a one-week washout period, and then receives the active medication for one week. The primary outcome is the average sleep onset latency, measured in minutes via polysomnography at the end of each treatment period. A preliminary analysis of the data reveals that the differences in sleep onset latency between the two treatment periods are markedly skewed and do not adhere to a normal distribution. Which of the following statistical tests is most appropriate to determine if there is a significant difference in sleep onset latency between the two treatments?

  1. Wilcoxon signed-rank testAnswer
  2. B
    Paired t-test
  3. C
    Mann-Whitney U test
  4. D
    Kruskal-Wallis test
  5. E
    McNemar test

Answer

Wilcoxon signed-rank test
The correct test is the Wilcoxon signed-rank test. The scenario describes a crossover study evaluating two treatments within the exact same patients, which means the data are paired. The primary outcome, sleep onset latency in minutes, is a continuous variable. However, because the differences between the paired values are markedly skewed, parametric tests (which assume normality) are contraindicated. The Wilcoxon signed-rank test is the appropriate non-parametric statistical method for analyzing differences in paired, continuous variables that do not follow a normal distribution.

Step-by-Step Solution

1
Determine the study design and the relationship between the groups being compared.
The study uses a crossover design where each patient receives both treatments, meaning the data are paired or matched.
Test selection depends fundamentally on whether the groups are independent or paired.
2
Identify the dependent (outcome) variable's data type.
The outcome is sleep onset latency measured in minutes, which is a continuous variable.
Different test families are required for continuous, ordinal, or categorical outcome variables.
3
Assess the distribution of the data.
The differences in sleep onset latency between the two periods are markedly skewed, violating the assumption of normality.
Parametric tests require normal distributions; significant skewness dictates the use of a non-parametric alternative.
4
Select the appropriate statistical test based on the collected parameters.
The Wilcoxon signed-rank test is selected because it is the non-parametric equivalent of the paired t-test, designed for two paired groups with a skewed continuous outcome.
This test ranks the absolute differences between the paired observations rather than analyzing the raw means, safely accommodating non-normal data.

Key Concept

Selection of the Wilcoxon signed-rank test for paired, continuous data with a non-normal distribution.
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Topics

Inferential Statistical Tests

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