Rank-Based Tests
Comparison tool
Compare groups by rank, for when the average is not a safe summary: skewed spend, ratings, or one customer who is nothing like the others.
📖 What a rank test actually does
A rank test lines every case up from smallest to largest and works with each case's position rather than its value. The largest order in the file is simply last in line, whether it is twice the next one or fifty times it.
That is the whole trade. You give up the ability to say by how much, and in return no single case can drag the answer around.
DATA SOURCE
📚
Use a Case Study
📊
Use Your Data
One row per case, with a column naming the group and a column holding the number. The tool reads the shape of your file and picks the design to match.
Drag & Drop your file (.csv, .tsv, .txt)
Headers like group,value. At least 6 rows.
One column per group also works and is detected automatically, so a spreadsheet laid out that way needs no rearranging. There is no template for it because long format is the shape worth learning: every other tool here reads it.
Messy file? The Import Wizard will check it and tell you what to fix. Files above about 5 MB are slow in the browser; take a sample of the rows instead.
No file uploaded.
One box per group. Paste a column from a spreadsheet, or type the numbers separated by spaces, commas or new lines. Good for the ten numbers on a whiteboard.
Nothing entered yet.
INPUTS & SETTINGS
What kind of comparison is this?
Pick by how the data was collected, not by the name of a test. The test follows from the answer.
Units on the values
Confidence level
Advanced
By default a pair that did not change is set aside before ranking, which is Wilcoxon's own method. Pratt's keeps them and gives a different p-value, so whichever you use has to be reported.
Nothing to set for this design.
Order of the groups
Drag to reorder, or use Alt and the arrow keys. This changes how the groups are listed and charted. It cannot change the test result.
How often would a gap this big show up by chance?
–p-value
Load a case to see what this means here.
How often is the higher group actually higher?
–Probability of superiority
What did the test itself come out at?
–Mann-Whitney U
Report it alongside the p-value, not instead of it.
Those three names are the ones you will be graded on. The questions above them are what each one is actually answering.
Start here
The same cases, by value and by rank
Each group
| Group | n | Median | Middle half | Mean rank | Mean |
|---|
Managerial Interpretation
Diagnostics & assumptions
What this test is assuming about your data
Nothing here needs your attention. A rank test asks less of the data than a t-test does, which is most of why you would reach for one.
Which pairs actually differ
| Comparison | Adjusted p | How often the higher one wins | Verdict |
|---|
Six comparisons on four groups means six chances to find something by accident, so each p-value is adjusted upward to pay for the extra looks. Read the overall test first: this table says which groups differ, not whether any do.
What the t-test says about the same data
Compare the two tests
| Test | p-value | Which group comes out ahead |
|---|---|---|
| Welch's t-test (compares averages) | ||
| Mann-Whitney (compares ranks) |
Nothing is deleted and nothing is downloaded. Both tests above re-run without that one case so you can see which of them it was moving.