Two-way Analysis of Variance
The following hypothetical example gives the yields of 15 plants subject to two different environmental variations, and three different fertilisers.
| Extra CO2 | Extra humidity | |
|---|---|---|
| No fertiliser | 7, 2, 1 | 7, 6 |
| Nitrate | 11, 6 | 10, 7, 3 |
| Phosphate | 5, 3, 4 | 11, 4 |
Five sums of squares are calculated:
| Factor | Calculation | Sum | |
|---|---|---|---|
| Individual | 641 | 15 | |
| Fertiliser × Environment | 556.1667 | 6 | |
| Fertiliser | 525.4 | 3 | |
| Environment | 519.2679 | 2 | |
| Composite | 504.6 | 1 |
Finally, the sums of squared deviations required for the analysis of variance can be calculated.
| Factor | Sum | Total | Environment | Fertiliser | Fertiliser × Environment | Residual | |
|---|---|---|---|---|---|---|---|
| Individual | 641 | 15 | 1 | 1 | |||
| Fertiliser × Environment | 556.1667 | 6 | 1 | −1 | |||
| Fertiliser | 525.4 | 3 | 1 | −1 | |||
| Environment | 519.2679 | 2 | 1 | −1 | |||
| Composite | 504.6 | 1 | −1 | −1 | −1 | 1 | |
| Squared deviations | 136.4 | 14.668 | 20.8 | 16.099 | 84.833 | ||
| Degrees of freedom | 14 | 1 | 2 | 2 | 9 |
Read more about this topic: Squared Deviations
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