Is that client really slower or just one late invoice?

Fifteen invoices each, measured from issue to cash. The rank test separates them almost completely, and the same data through a means test is 270 times weaker, which is a lesson about payment data rather than about these two clients.

Words on this sheet

  • Median: The middle value: half the readings sit above it and half below.

Finance Starter Statistics free

After you install, this is the model to open.

Do These Two Clients Pay at the Same Speed?

  1. In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
  2. Click Start from a template and put that name in the search box.
  3. Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.

The answer

The rank test, and the same data through a means test:

p-value
0.0000045 U 1.5, z -4.59
Pairwise comparisons
225 slower in all but 1.5
Means test on the same data
0.0012 270 times weaker
What did it
one 86-day invoice

The single invoice that most proves your point is the one that most weakens a means test: 86 days lifts the slower client's average from 30.93 to 34.60 and inflates the variance the test has to divide by. A rank test only cares that 86 is the largest value in the pool, not by how much, so one dispute cannot bully the result. Payment data is skewed by construction, because an invoice can be paid very late but never earlier than the day it was issued, and skew is the condition this test was built for. Report the medians: 18 days against 30 is the honest summary and the one a credit controller can act on.

The model

One client per column, fifteen invoices each, independent rather than paired. The Mann-Whitney test compares every invoice against every invoice rather than comparing two averages.

Clients2
Invoices each15
Measuredays from issue to cash
Medians18 days against 30
U, z and pcalculated

Once it is in your sheet

  1. The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
  2. Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
  3. Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.

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