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
Famous quotes containing the words two-way, analysis and/or variance:
“Think of the child’s question as the start of a two-way conversation rather than a question-and-answer session. Sometimes it may be necessary to learn what children think about the subject and what misconceptions they may have before providing an answer.”
—Ruth Formanek (20th century)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)
“There is an untroubled harmony in everything, a full consonance in nature; only in our illusory freedom do we feel at variance with it.”
—Fyodor Tyutchev (1803–1873)