Tag: statistical summary

CougarStats: a free and open-source Statistics web app for Teaching and Learning

Hello,

I’d like to share CougarStats, a free and open-source R Shiny web app I developed to support the teaching and learning of Statistics. CougarStats runs entirely in a browser and is designed for accessibility and ease of use. You can explore the app here: https://www.cougarstats.ca/ 
 
The name CougarStats is inspired by Mount Royal University’s athletics mascot, the cougar, symbolizing strength and agility, and by the app’s focus on statistics. 
 
Key features of CougarStats
 
  • Descriptive Statistics: Compute measures like mean, median, mode, quartiles, IQR, standard deviation, and identify potential outliers. 
  • Data Visualization: Construct Boxplots, Histograms, and Scatterplots. 
  • Probability: Calculate marginal, joint, union, and conditional probability for contingency tables; exact and cumulative probabilities for Binomial, Poisson, Negative Binomial and Hypergeometric distributions; and cumulative probabilities for the Normal distribution. 
  • Sample Size Estimation: Determine the required sample sizes for various scenarios. 
  • Statistical Inference: Construct confidence intervals, conduct hypothesis tests for one- and two-samples (mean, proportion and standard deviation). 
  • ANOVA: Perform one-way Analysis of Variance with an option to conduct Bonferroni post hoc tests. 
  • Regression and Correlation: Fit simple linear regression models and compute Pearson correlation coefficient, multiple linear regression, logistic regression. 
  • Categorical Data Analysis: Perform Chi-Square test of independence with and without Yates’ continuity correction, Fisher’s exact test. 
  • Nonparametric Tests: Perform the Mann-Whitney U Test, Kruskal-Wallis test etc.
 
I would be delighted if you could explore CougarStats and share it with your students and colleagues who might find it useful.
 
Thank you for your time, and I look forward to hearing your thoughts.
 
Sincerely, 
Ashok

—
Ashok Krishnamurthy, PhD
Associate Professor
Department of Mathematics and Computing
Mount Royal University
4825 Mount Royal Gate SW
Calgary, AB, T3E 6K6 Canada

Understanding R’s `describe()` Function: A Complete Guide to Summary Statistics

Understanding R’s describe() Function: A Complete Guide to Summary Statistics

Table of Contents

  1. Introduction to describe()
  2. Breaking Down the Output Columns
  3. Key Statistics and Their Interpretation
  4. Practical Examples
  5. When to Use Which Statistic
  6. Extending the Functionality
  7. Conclusion

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:

Column Description Formula/Calculation Ideal Use Case
vars Variable index number – Tracking variable order
n Complete cases length(na.omit(x)) Data completeness check
mean Arithmetic average sum(x)/n Normally distributed data
sd Standard deviation sqrt(var(x)) Measuring spread
median 50th percentile quantile(x, 0.5) Skewed distributions
trimmed Mean after removing extremes mean(x, trim=0.1) Robust central tendency
mad Median absolute deviation median(abs(x-median(x))) Outlier-resistant spread
min Minimum value min(x) Range assessment
max Maximum value max(x) Range assessment
range Max – Min max(x)-min(x) Total spread
skew Distribution asymmetry sum((x-mean(x))³)/(n*sd(x)³) Detecting skew direction
kurtosis Tailedness sum((x-mean(x))⁴)/(n*sd(x)⁴)-3 Outlier propensity
se Standard error sd(x)/sqrt(n) Precision of mean estimate

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

Scenario Recommended Statistics
Normal Distribution Mean, SD
Skewed Data Median, IQR, MAD
Outlier Detection MAD, trimmed mean, kurtosis
Parametric Testing Mean, SE
Nonparametric Analysis Median, IQR

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!

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