Two machines, same average. Which one wanders?
Both machines aim at 250 mm and both hit it on average, which is why a t-test finds nothing here. The difference is wander, and the F-test is the tool that compares wander.
Operations Starter Statistics free
After you install, this is the model to open.
Is the New Machine More Consistent?
- 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 ratio is enormous and the p-value backs it:
- F statistic
- 95.61
- p (one-tail)
- 0.000002
- Tightening
- 10x in std deviation
A ten-fold tightening in standard deviation is the difference between parts that need rework and parts that just fit. The F-test moonlights as a pre-check too: run it before any two-group t-test, and when it comes back significant like this, use the Welch version for the means.
The model
Eight cut lengths from the old saw and eight from its proposed replacement, both targeting 250 mm. The F statistic is simply the ratio of the two sample variances.
| Old machine | sd 2.40 mm |
| New machine | sd 0.24 mm |
| Means | both ~250 mm |
| F 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.
Next question
- What is next month's demand, give or take?Smooth the Noise, See the Trend
- Is overselling worth the bumps at the gate?How Many Tickets Should You Oversell?
- How often will the reserve you set fall short?Is the Warranty Reserve Enough?
- How many people will the peak month need?Staff for the Season, Not the Average
- How far above average demand should you order?How Many Should I Order?
- What does staffing to an average day cost you?How Many People Should Be on Shift?
Every model like this one, and the method behind them: Statistics in Google Sheets.