You changed two things and it worked. Which one did it?
Bake in a better oven with a better recipe and the loaf improves, but which change did the work? With repeats of every combination, two-factor ANOVA separates the two effects and catches the part where they conspire.
Home Starter Statistics free
After you install, this is the model to open.
Oven, Recipe, or Both?
- 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
Three F-tests from one grid, and all three come back real:
- Recipe
- F 90.75 p 0.00001
- Oven
- F 36.75 p 0.0003
- Interaction
- F 18.75 p 0.0025
The interaction is the finding a one-factor test would have averaged away: convection lifts sourdough by about 0.6 cm but rye by barely 0.1, so "which oven?" has no answer until you name the recipe. Any two-factor question with repeats fits the same grid: machine and material, region and offer, shift and product.
The model
A weekend experiment: two recipes across the columns, two ovens down the rows, three loaves of every combination, rise in centimeters. Three measurements per cell is what lets the interaction term exist.
| Factors | Oven (deck, convection) x Recipe (sourdough, rye) |
| Replication | 3 loaves per combination |
| Recipe effect | calculated |
| Oven effect | calculated |
| Interaction | 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.
The method behind this one, worked end to end: ANOVA in Google Sheets.