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Difficulty: HardData Types, Distributions, and Descriptive Statistics

A research team is analyzing serum neuronal enriched enolase (NEE) concentrations (measured in ng/mL\text{ng/mL}) collected from 800800 patients following out-of-hospital cardiac arrest. The dataset reveals a mean NEE concentration of 45 ng/mL45 \text{ ng/mL}, a median of 18 ng/mL18 \text{ ng/mL}, and a mode of 12 ng/mL12 \text{ ng/mL}. The standard deviation is reported as 52 ng/mL52 \text{ ng/mL}. The researchers are preparing the manuscript's methods section regarding how they will summarize this baseline characteristic and compare it between patients who achieved return of spontaneous circulation and those who did not. Based on the descriptive statistics provided, which of the following is the most appropriate methodological approach?

  1. Report the median and interquartile range due to the positive skew of the distribution, and select a non-parametric test for group comparisons.Answer
  2. B
    Report the mean and standard deviation due to the negative skew of the distribution, and select a parametric test for group comparisons.
  3. C
    Convert the measurements into an ordinal scale because continuous variables cannot be analyzed when the standard deviation exceeds the mean.
  4. D
    Report the mean and standard deviation because the sample size is sufficiently large to normalize the underlying data distribution via the Central Limit Theorem.
  5. E
    Apply the empirical rule to estimate that 16%16\% of the cohort has negative serum concentrations, and exclude these physiologically impossible values before analysis.

Answer

The most appropriate approach is to report the median and interquartile range because the data exhibits a positive skew, and to utilize a non-parametric test for group comparisons.
The correct approach recognizes that a mean significantly higher than the median and mode indicates a positively (right) skewed distribution. For such skewed continuous variables, the median is a more robust measure of central tendency than the mean, and the interquartile range is preferred over the standard deviation for reporting dispersion. Additionally, non-parametric statistical tests are appropriate for comparing groups when the underlying data is heavily skewed.

Step-by-Step Solution

1
Analyze the relationship between the measures of central tendency.
The mean (4545) is significantly greater than the median (1818), which is greater than the mode (1212).
Comparing the mean, median, and mode reveals the shape and symmetry of the data distribution.
2
Identify the distribution shape.
The data exhibits a strong positive (right) skew.
When the mean is pulled disproportionately toward higher values compared to the median and mode, it indicates a long right tail (positive skew).
3
Determine the appropriate descriptive statistics and test selection.
For highly skewed continuous data, the median and interquartile range (IQR) should be used, and non-parametric tests should be utilized for comparisons.
The mean and standard deviation are heavily influenced by extreme values in the skewed tail and would misrepresent the typical patient's baseline value. Non-parametric tests do not assume a normal distribution.

Key Concept

Continuous data with a positive (right) skew (Mean > Median > Mode) should be summarized using the median and interquartile range rather than the mean and standard deviation. The Central Limit Theorem applies to the sampling distribution of the mean, not the underlying data distribution.
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Topics

Data Types, Distributions, and Descriptive Statistics

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