Distribution
Empirical cumulative distribution plot (ECDF)
Shows the proportion of observations less than or equal to each value.
- Plot
- Distribution
- Cumulative probability
What it answers
What proportion is at or below a threshold?
- Shape
- Non-decreasing step curve
- What it shows
- Percentiles and threshold attainment.
Example
The question
What share of orders ship within a given number of hours?
Share of orders shipped within each number of hours (ECDF, illustrative)
Illustrative data. It belongs to no company.
When to use it
Use it when
Distribution comparisons without choosing bins.
Avoid it when
When readers confuse cumulative probability with frequency density.
How to read it
Read a value on X and the step height as cumulative proportion.
The data you need
- Layout
- Long table
- Fields
- Value: number
- One row is
- One raw numeric observation. What is the grain?
- Rules
- Use raw observations unless the chosen renderer explicitly accepts summaries or bins. Define missing-value treatment.
- Optional
- Optional frequency Weight. Pre-binned alternative: BinStart,BinEnd,Count; do not treat counts as raw values.
- Preparation
- Keep raw numeric observations, group them if needed and handle missingness explicitly. Choose bins, bandwidth or summary conventions as appropriate to this specific plot.
- Units
- Y is count(Value<=threshold)/eligible nonmissing observations; ranges 0-1 or 0-100%.
Worked example
Values 10,12,12,18,23. At 12 the ECDF is 3/5=60%; at 18 it is 4/5=80%.
| Value |
|---|
| 10 |
| 12 |
| 12 |
| 18 |
| 23 |