Squared Deviations - Two-way Analysis of Variance

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)

    ... the big courageous acts of life are those one never hears of and only suspects from having been through like experience. It takes real courage to do battle in the unspectacular task. We always listen for the applause of our co-workers. He is courageous who plods on, unlettered and unknown.... In the last analysis it is this courage, developing between man and his limitations, that brings success.
    Alice Foote MacDougall (1867–1945)

    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)