Introduction to describe()

The describe() function from R’s psych package (Revelle, 2023) provides a comprehensive statistical summary of your dataset. Unlike R’s base summary() function, it includes additional metrics that are particularly useful for data exploration and assumption checking.

library(psych)
describe(your_data)

Breaking Down the Output Columns

Here’s what each column in the output represents:

Key Statistics and Their Interpretation

Central Tendency

• Mean vs. Median: Differences indicate skewness
• Trimmed Mean: Removes influence of outliers (default drops top/bottom 10%)

Variability

• SD vs. MAD: Use MAD when outliers are present
• Range: Simple but outlier-sensitive

Distribution Shape

• Skewness:
  • >0: Right-tailed
  • <0: Left-tailed
  • 0: Symmetric
• Kurtosis (Excess):
  • >0: Heavy-tailed (more outliers than normal)
  • <0: Light-tailed

Practical Examples

Example 1: MPG from mtcars

describe(mtcars$mpg)

Output Interpretation:

   vars  n   mean    sd median trimmed   mad min  max range skew kurtosis   se
1     1 32 20.09 6.03   19.2   19.70 5.41 10.4 33.9  23.5 0.61    -0.37 1.07

• Right-skewed (mean > median, positive skew)
• Light-tailed (negative kurtosis)
• SD (6.03) > MAD (5.41): Suggests some outlier influence

When to Use Which Statistic

Extending the Functionality

Adding IQR

The default describe() doesn’t show IQR, but you can add it:

library(dplyr)
describe(mtcars) %>% 
  mutate(IQR = apply(mtcars, 2, IQR, na.rm = TRUE))

Comparing Groups

Use describeBy() for grouped statistics:

describeBy(mtcars$mpg, group = mtcars$cyl)

Conclusion

R’s describe() function provides a powerful starting point for exploratory data analysis. By understanding each statistic it provides, you can:

• Detect data quality issues
• Choose appropriate analysis methods
• Understand your variables’ distributions
• Make informed decisions about data transformations

For formal reporting, consider supplementing these metrics with visualization and statistical tests.

Pro Tip: Always visualize your data alongside these statistics – numbers tell part of the story, but plots reveal the full picture!

Happy coding!

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Reference:
Revelle, W. (2023). psych: Procedures for Psychological, Psychometric, and Personality Research. Northwestern University.