Is one line underfilling, or is that just spread?
When months of process history already document each line's variance, estimating spread from eight bottles throws information away. The z-test takes the known variances and sharpens the verdict on the means.
Words on this sheet
- Production line: One of the parallel lines being compared. Each is a separate machine or crew, so a reading from one is not a reading from the other.
Operations Starter Statistics free
After you install, this is the model to open.
Are Two Fill Lines Filling the Same?
- 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 processes this tight, 1.2 grams is a verdict, not noise:
- z statistic
- 3.60
- p (two-tail)
- 0.0003
- Action
- adjust Line 2 filler head
Line 2 is genuinely underfilling relative to Line 1, a 1.2 g gap that chance would produce about three times in ten thousand. The honest caveat cuts the other way: if you do not have documented variances, do not invent them, use the two-sample t-test, which estimates spread from the data it actually sees.
The model
Eight fill weights from each of two lines targeting 500 g, with documented variances 0.25 and 0.64 typed into the form rather than estimated from the sample.
| Line 1 | mean 500.23 g, known variance 0.25 |
| Line 2 | mean 499.03 g, known variance 0.64 |
| Gap | 1.2 g |
| z 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
- Two machines, same average. Which one wanders?Is the New Machine More Consistent?
- 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?
Every model like this one, and the method behind them: Statistics in Google Sheets.