4. This is an example of using orthogonal polynomials to analyze data from de- t

Question

4. This is an example of using orthogonal polynomials to analyze data from de- t in which the treatmer design consisted of five plant densities (-10, 20, 30, 40 and 50 plants per unit of area), each replicated three (r-3) times in a completely randomized design The numbers in the body of the table below are the responses, plant yield per unit of area: Table 1: Plant Density (x) 10 20 30 40 50 12.2 16.0 18.6 17.6 18.0 11.4 15.5 20.2 19.3 16.4 12.4 16.5 18.2 17.1 16.6 Means 12.0 16.0 19.0 18.0 17.0

Explanation / Answer

Calculating the orthogonal polynomial coefficients, we get:

P0 = 1 = Mean

P1 = (-2, -1, 0, 1, 2) = Linear

P2 = (2, -1, -2, -1, 2) = Quadratic

P3 = (-6/5, 12/5, 0, -12/5, 6/5) = Cubic

Substituting and comparing either predictions should give the same result and hence both predications are identical.

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