Empirical CDF
Chart overview
The empirical CDF plots each sorted observation against its cumulative probability, producing a step function that converges to the true CDF with increasing sample size.
Key points
- Unlike histograms, the ECDF requires no binning decisions and retains all data points, making it the preferred method for comparing distributions in statistics and data science.
- It is commonly used alongside the Q-Q plot and two-sample Kolmogorov-Smirnov tests to assess distributional differences.
Example Visualization
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"Create an empirical CDF plot from my data. Plot the step function for each group or variable using distinct colors, add horizontal reference lines at the 25th, 50th, and 75th percentiles, overlay a fitted theoretical CDF if requested, and include a legend with sample sizes."
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Python Code Example
Console Output
Figure saved: plotivy-empirical-cdf.png
Common Use Cases
- 1Comparing gene expression distributions across experimental conditions without histogram bins
- 2Visualizing the distribution of model prediction errors for multiple algorithms
- 3Assessing whether patient survival times differ between treatment groups
- 4Summarizing particle size distributions in materials science or soil science samples
Pro Tips
Use drawstyle steps-post in matplotlib to correctly represent the ECDF step function
Overlay multiple groups on the same axes rather than separate panels to ease comparison
Add vertical lines at key quantiles (median, quartiles) with dashed lines and text labels
Show pointwise 95% confidence bands for small sample sizes using the DKW inequality
Scientific Chart Selection Cheat Sheet
Not sure whether to use a Violin Plot, Box Plot, or Ridge Plot? Download our single-page reference mapping the most-used scientific chart types, exactly when to use them, and the core Matplotlib/Seaborn functions.