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Difficulty: Very hardInferential Statistical Tests

A dermatology research team conducts a study comparing the efficacy of two topical immunomodulators, Agent X and Agent Y, for the treatment of severe atopic dermatitis. The study enrolls 1818 adult patients who present with symmetrical, similarly severe eczematous lesions on both their left and right antecubital fossae. For each patient, the investigators randomly assign Agent X to one arm and Agent Y to the contralateral arm.

After 66 weeks of twice-daily application, the researchers measure the absolute reduction in the Eczema Area and Severity Index (EASI) score for each arm. Statistical evaluation reveals that the reduction scores for both treatment arms are severely non-normally distributed with a pronounced right skew. The researchers wish to determine if there is a statistically significant difference in the reduction of disease severity between the two topical treatments.

Which of the following is the most appropriate statistical test to perform this analysis?

  1. A
    Mann-Whitney U test
  2. B
    Paired Student's t-test
  3. Wilcoxon signed-rank testAnswer
  4. D
    Independent samples Student's t-test
  5. E
    Kruskal-Wallis test

Answer

The Wilcoxon signed-rank test is the most appropriate statistical test for this analysis.
The study design involves testing two different treatments on the same individuals (a split-body design), which means the data are dependent or paired. Because the sample size is small (n=18n=18) and the data are severely non-normally distributed, parametric testing is invalid. The Wilcoxon signed-rank test is the appropriate non-parametric statistical test to compare two paired groups of continuous data that do not meet the assumption of normality.

Step-by-Step Solution

1
Identify the type of data being analyzed.
The outcome variable is the absolute reduction in EASI score, which is a continuous numeric variable.
Determining the data type is the first step in selecting the correct statistical test.
2
Assess the relationship between the two comparison groups.
The study uses a split-body design (Agent X on one arm, Agent Y on the other arm of the same patient). Therefore, the data points between the two groups are dependent (paired).
Tests for independent groups differ fundamentally from tests for paired data.
3
Evaluate the distribution of the data.
The sample size is small (n=18n=18) and the data are severely non-normally distributed.
Parametric tests assume normal distribution; severe skewness in a small sample necessitates a non-parametric alternative.
4
Select the appropriate statistical test based on the established parameters.
The Wilcoxon signed-rank test is identified as the correct test.
It is the specific non-parametric test designed to compare two dependent (paired) groups of continuous data.

Key Concept

Statistical test selection based on data type, group dependency (paired vs. independent), and distribution normality.
Estimated Time:1m 15s
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Topics

Inferential Statistical Tests

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