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Probability Distributions And Alternative Transformations Of Soil Test NO3-N And PO4-P, Implications For Precision Agriculture
A. Moulin
Agriculture and Agri-Food Canada
Recommendations for fertilizer N in crop production and precision agriculture depend on statistical analyses of data which represent soil NO3-N and PO4-P fertility typical of management zones and fields. Non-normal distributions of soil test N are commonly log transformed prior to statistical analysis for interpolation with methods such as kriging, regression, or principle component analysis. These data are transformed to ensure that analysis meet the assumptions of normality for the distribution of data and equality of variances. Analyses of soil test NO3-N and PO4-P in the 0-15 cm depth increment for samples (48 to 100 sites per field) in 8 fields in Manitoba identified a range of distributions including the lognormal, exponential, Johnson lognormal and Gamma. Mixed distributions consisting of 2 normal functions combined were also observed for some landforms. No single distribution characterized soil NO3-N for all landforms or fields, and the distribution functions considerably by field and by landform. The consequences of this wide range of distributions are significant, as the calculation of moments such as the mean or standard deviation based on the normal distribution for untransformed data will result in biased estimates of parameters for soil properties. The normal quantile transformation is an alternative to those based on other functions. The transformation assigns a normal quantile value to each of ranked data, resulting in a normal distribution. However the normal quantile transformation should be applied with caution to parametric analysis such as analysis of variance or principle components analysis, as the results of analyses cannot be back-transformed to means or standard deviations. Continuous functions such as the Johnson Sl, Generalized Log or normal quantile may be useful as alternatives to the lognormal in transforming data, in order to take advantage of the wide range of options for parametric analyses in analysis of variance, regression and principle component analysis. Furthermore these transformations will improve recommendations for N fertilizer based on soil test as the central moment is representative of the soil property for the spatial scale in question. However each transformation should be evaluated on a case-by-case basis with respect to the statistical analysis, soil property, spatial scale, and landform in question.
A. Moulin
Spatial Variability in Crop, Soil and Natural Resources
Poster
2014
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