Two crews average the same. Is one of them better?
Four shift crews, eight days each, units packed. Two crews have almost identical averages and the rank test separates them cleanly, because one of those averages is a single 289-unit day in disguise.
Words on this sheet
- Mean: The average: everything added up and divided by how many there are.
- Median: The middle value: half the readings sit above it and half below.
Operations Intermediate Statistics free
After you install, this is the model to open.
Four Shifts, Ranked Output, One Question
- 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.
- Click Start from a template and put that name in the search box.
- 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
- On the monthly report
- 212 vs 212 Crew A and Crew D average the same units
- The rank verdict
- p = 0.0004 H = 18.14: the four crews are not interchangeable
- The real order
- 232 to 197.5 median units: C, then A, then D, then B
- A against D alone
- p = 0.16 eight days cannot convict a single pair yet
Four crews, eight days each, units packed. Look at the Mean line in the small block beside the data first: Crew A averages 212.00 and Crew D averages 212.13, so on the monthly report they are the same crew. Click Run: H comes back 18.14 on 3 degrees of freedom with a p-value of 0.00041, and the mean-rank column tells a completely different story from the means.
Crew C sits at 27.13, Crew A at 17.75, Crew D at 13.25 and Crew B at 7.88. Crew A and Crew D are not the same crew at all: A outranks D by four and a half places on average. The reason is the single 289-unit day sitting in Crew D's column, the day it had agency staff in to clear a backlog. That one day carries Crew D's mean up to match Crew A while its other seven days sit below.
A rank test cannot be moved that way, because 289 counts as the highest value in the pool and nothing more, so Crew D's median of 202.5 against Crew A's 212.5 survives into the answer. That is the whole argument for using a rank test on operational data: one unusual shift is normal, and any statistic that lets one shift set the answer will be wrong about crews in exactly the situations where the question was worth asking.
Kruskal-Wallis tells you the four crews are not interchangeable and does not tell you which pairs differ, so follow it with Mann-Whitney on the two you care about. On Crew A against Crew D it returns a two-tail p-value of 0.161, which does not clear the bar: eight days is enough evidence to say the four crews differ overall and not enough to convict any single pair.
That is the normal relationship between an overall test and the pairwise ones that follow it, and it means nobody gets spoken to until there are more days on the sheet. One more run worth doing. Replace the 289 with Crew D's own median of 202.5 and H rises to 21.71 rather than falling, because taking the freak day out makes Crew D's real position clearer rather than muddier.
Removing an outlier is not the same as softening a result. To use your own line, put one crew per column with the crew name in the header row and widen the range.
The model
It arrives on a tab called Template: Four Shifts, Ranked, carrying these columns:
- Crew A (units packed)
- Crew B (units packed)
- Crew C (units packed)
- Crew D (units packed)
with the model computed beside the data:
| Mean | 212 |
| Median | 212.5 |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- 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.
- 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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Every model like this one, and the method behind them: Statistics in Google Sheets.
The method behind this one, worked end to end: ANOVA in Google Sheets, and Kruskal-Wallis beside it.