Three averages differ. Is that more than chance?
Group averages differ in every experiment ever run; three random groups would differ too. ANOVA asks the only question that matters: are these gaps bigger than chance can explain?
School Starter Statistics free
After you install, this is the model to open.
Which Study Method Actually Works?
- 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 between-group gap dwarfs the within-group noise:
- F statistic
- 24.15
- F critical
- 3.68
- p-value
- 0.00002
- Best vs worst gap
- 12.8 points
Random grouping produces gaps this size about twice in a hundred thousand tries, so the method genuinely matters, and practice tests finish almost thirteen points clear of rereading. ANOVA says THAT the groups differ, not which pairs; follow with a t-test between any two columns for the pairwise verdict. Swap in suppliers, ad creatives, or class sections.
The model
Eighteen students split across flashcards, rereading, and practice tests, six per group, one exam. One column per method; ANOVA compares the variation between groups to the variation within them.
| Flashcards | mean 82.8 |
| Rereading | mean 76.0 |
| Practice tests | mean 88.8 |
| F statistic 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.
The method behind this one, worked end to end: ANOVA in Google Sheets.