Calibration and assessment of soil tests for estimating fertilizer requirements. I. Statistical models and tests of significance.

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Abstract
The calibration of soil tests requires a statistical model to describe the relationship between yield of crop, fertilizer application rate, and soil test. Yield response to fertilizers can be represented by polynomials both in the natural and square-root scales, and these polynomials can be generalized for a given crop and region, using soil test expressions. The generalization can be done using orthogonal polynomials and simultaneous regression equations that relate the coefficients of the polynomials to the soil test variables. This procedure is necessary because of heterogeneity in the residual sum of squares of regressions fitted to the yield data of several fertilizer field experiments within a region. The set of simultaneous regression equations constitutes a direct calibration of the soil test, since it can be used for the estimation of economic fertilizer requirement. Highly significant calibrations are demonstrated for a phosphorus soil test with wheat and a potassium test with potatoes. A nitrogen test gave only non-significant (P > 0.05) relationships.

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