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Difficulty: MediumInferential Statistical Tests

A team of researchers is designing a prospective cohort study to investigate the relationship between a novel serum biomarker (measured in ng/mL) and the development of acute respiratory distress syndrome (ARDS) in patients admitted with severe sepsis. They plan to classify the enrolled patients into three independent categories based on their initial sequential organ failure assessment (SOFA) score: mild risk, moderate risk, and high risk. The serum biomarker will be measured once upon admission for all patients. The researchers are meeting to finalize the statistical analysis plan for comparing the continuous biomarker data across these three distinct risk groups. Which of the following statements regarding the appropriate statistical analysis for this study are correct? (Select all that apply)

  1. If the biomarker measurements within each risk group follow a normal distribution and have similar variances, a one-way analysis of variance (ANOVA) is the correct test to use.Answer
  2. If the biomarker measurements demonstrate a markedly skewed, non-normal distribution, the Kruskal-Wallis test is the most appropriate statistical method.Answer
  3. C
    A paired t-test is the preferred statistical method for directly comparing the mean biomarker levels between the mild risk and high risk groups.
  4. D
    The Pearson chi-square test should be utilized to evaluate if the mean biomarker levels differ significantly across the three risk categories.
  5. E
    If a one-way ANOVA is performed and yields a p-value of 0.03, the result definitively identifies which specific risk groups have significantly different biomarker levels.

Answer

The correct statements are that one-way ANOVA should be used for normally distributed continuous data across three or more independent groups, and the Kruskal-Wallis test should be used if the continuous data are non-normal or skewed.
The correct statements accurately reflect the rules for test selection when comparing a continuous variable across three or more independent groups. One-way ANOVA is the standard parametric approach when data are normally distributed. When data violate the assumption of normality (e.g., skewed distribution), the Kruskal-Wallis test serves as the appropriate non-parametric alternative.

Step-by-Step Solution

1
Identify the independent and dependent variables in the study design.
The independent variable is the risk category (categorical: 3 independent groups). The dependent variable is the serum biomarker level (continuous: ng/mL).
Variable types dictate which statistical tests are mathematically appropriate.
2
Determine the appropriate test for normal parametric data.
Comparing a continuous variable across 3 independent groups requires a one-way ANOVA, assuming normal distribution and equal variances.
ANOVA compares the means of three or more independent groups.
3
Determine the appropriate test for non-normal non-parametric data.
If the continuous data is skewed, the Kruskal-Wallis test must be used.
Kruskal-Wallis is the non-parametric equivalent to one-way ANOVA.
4
Evaluate the distractors based on test assumptions.
Chi-square is for categorical data. Paired t-test is for matched data. A significant ANOVA requires post-hoc testing to find pairwise differences.
Ruling out inappropriate tests based on their foundational assumptions.

Key Concept

Selecting inferential statistical tests based on variable type (continuous vs. categorical), group independence, and data distribution.
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Topics

Inferential Statistical Tests

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