Same average fill. So why is one supplier a risk?
Twelve fill-weight checks from each of two suppliers. Their averages are within half a gram of each other and one of them is five times more variable, which is the difference between a giveaway problem and a recall.
Operations Intermediate Statistics free
After you install, this is the model to open.
Which Supplier Is 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
- Variance ratio
- 29x Merrick 49.5 against Ardley 1.7
- In grams
- 7.04 vs 1.30 standard deviation on the same 500 g pack
- Chance says
- p = 0.0000015 one-tail F-test, twelve checks a side
- The averages
- 500.4 vs 500.0 why a means comparison missed it
Twelve fill-weight checks from each of two suppliers on the same 500 gram pack. Ardley averages 499.96 grams and Merrick averages 500.38, and if you stopped there you would conclude that Merrick is very slightly the better filler. Click Run: F comes back 0.034 with a one-tail p-value of 0.0000015. Ardley's variance is 1.70 and Merrick's is 49.51, so Merrick is 29 times more variable, which on the scale people actually picture is 5.4 times the standard deviation, 1.30 grams against 7.04.
That is not a rounding difference, it is a different process. Read the two under-the-minimum counters beside the data for what it costs. Nothing Ardley shipped went below the 491 gram legal minimum. One of the twelve Merrick lots did, at 489.7 grams, and a pack below the legal floor is not a quality metric, it is a recall and a regulator.
Merrick also runs the heavier average, so it is giving product away at the top of the same distribution that is failing at the bottom, and both of those are the same problem. Neither of them shows up in a comparison of averages. That is the whole reason this test exists as a separate tool: which supplier is better on average and which supplier is under control are different questions, and the second one is usually the expensive one.
Note that the reported F of 0.034 sits below its critical value of 0.355 rather than above it, because variable 1 here is the tighter supplier. Swap the two ranges over and you get 29.20 against a critical value of 2.818, with exactly the same p-value: it is the same test either way round, and only the direction of the ratio changes. Many two-sample t-tests assume the two spreads match, so this is also the run to do before choosing between the equal-variances version and the Welch version.
Twelve checks each is enough here only because the gap is enormous; two processes that genuinely differ by a factor of one and a half would need several times as many lots before this test could say so. To use your own data, paste one supplier per column and widen both ranges.
The model
It arrives on a tab called Template: Which Supplier Is More Consistent, carrying these columns:
- Lot
- Ardley fill weight (g)
- Lot
- Merrick fill weight (g)
- 500
with the model computed beside the data:
| Ardley lots under the minimum | 0 |
| Merrick lots under the minimum | 1 |
| Ardley average giveaway (g) | -0.04167 |
| Merrick average giveaway (g) | 0.3833 |
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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