Median and Interquartile Range (IQR)
For a small sample of 15 subjects measuring incubation period days, the data should be expressed as median and interquartile range (IQR), not mean and standard deviation.
Rationale for This Recommendation
Why Median and IQR Are Appropriate
Incubation periods follow non-normal distributions: Research consistently demonstrates that incubation periods for infectious diseases follow log-normal distributions rather than normal distributions 1, 2, 3.
Small sample size increases vulnerability to outliers: With only 15 subjects, a single extreme value can dramatically skew the mean and inflate the standard deviation, making these measures misleading 1.
Median provides robust central tendency: The median represents the 50th percentile and is not influenced by extreme values, making it ideal for skewed distributions like incubation periods 4.
IQR captures meaningful spread: The interquartile range (25th to 75th percentile) describes the middle 50% of data and is resistant to outliers, providing a more accurate representation of typical variation 4.
Why Mean and SD Are Inappropriate
Assumes normal distribution: Mean and standard deviation are only appropriate for normally distributed data, which incubation periods are not 1, 3.
Sensitive to outliers: In small samples with skewed data, the mean can be pulled toward extreme values, misrepresenting the typical case 2.
May produce impossible values: For incubation periods, mean minus one standard deviation could theoretically produce negative values, which is biologically impossible 1.
Why Other Options Don't Apply
Pearson coefficient: This measures linear correlation between two variables, not the distribution of a single variable like incubation period 4.
t-test: This is an inferential statistical test for comparing means between groups, not a descriptive statistic for expressing data distribution 4.
Practical Application
When reporting your 15 subjects' incubation periods, present them as: "Median incubation period was X days (IQR: Y-Z days)" 4. This format is standard in medical literature for time-to-event data and provides clinically interpretable information about both the typical case (median) and the range of variation (IQR).