One group is wild, one is steady. Is the gap real?
The ordinary t-test assumes both groups wobble alike. Operations data rarely obliges. Welch's test adjusts its confidence to what the data can honestly support, and stays truthful when spreads differ a hundred-fold.
Work Starter Statistics free
After you install, this is the model to open.
Manual vs Automated, Tested Fairly
- 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
The fifteen-minute saving holds up under the honest test:
- t statistic
- 5.38
- p (two-tail)
- 0.001
- Variance ratio
- 100x
- Time saved
- 15.3 min/invoice
Automation did not just move the average, it removed the 38-minute disasters entirely, and the variances tell you that before any test does. Reach for Welch whenever one group is wilder than the other, which in real operations data is most of the time; when in doubt, it is the safer default.
The model
Eight invoices processed by hand against eight through the automated flow. The variances differ by a factor of a hundred (64.3 vs 0.64), exactly the situation the standard test misstates.
| Manual | mean 25.0 min, variance 64.3 |
| Automated | mean 9.66 min, variance 0.64 |
| Welch df | calculated |
| t and p-value | calculated |
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.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
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Every model like this one, and the method behind them: Statistics in Google Sheets.