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Median and quantile

Rhizoctonia symptomes on sugar beets Ahead of an analysis of hyperspectral information with advanced statistical procedures it it more useful to archive a common overview by using median and 95% quantile calculations. The dynamics of most stresses are starting with a lag phase, followed by rapid changes, and a final approximation to an upper or lower asymptote. The time courses are fitted well by sigmoidal functions. Early stress responses are detectable by small changes of the hyperspectral signal, but not all crops respond in the same at the same time. The natural variance is easily recorded and shown by hyperspectral measurement technique. Hyperspectral data1 were taken from Rhizoctonia solani experiments on sugar beets as an example. The high pathogenicity of the fungi has the potential to demonstrate the complete range (and boundaries) of possible signatures. A stress free population, for example a field or all crops of a factorial experiment, show high light absorption in the visible domains contemporary with a low and symmetric variance. (fig. 1, yellow signature)

Hyperspectral signatures of Rhizoctonia solani
Fig. 1: Change of hyperspectral signatures with disease progress
Stress affects just single crops in the beginning, the median does not change much, but the 95% corridor of the quantile enlarges in the visible domains. The distribution is not any more symmetrical, but left skewed. With disease progress the median is changing to the pattern shown in fig. 1. Initially just a few plants are affected by the stress, the median changes marginal in such cases, but the 95% confidence interval enlarges mainly in the visible domains. The distribution is left skewed. Further stress progress yield in changed medians with symmetrical, but larger variance. More plants are affected by the fungi. A the stage of heavy infestation describes the condition of some lethal crops, the median signature demonstrates further changes in the visible domains. The distribution is right skewed now. At a final stage, all crops are more or less destroyed, the signal describes more or less the bare soil. But the distribution is symmetrical again. Not surprising as no green tissue exists anymore. 

Rizoctonia is one of those extreme pathogens, the complete destruction of all crops are not to find that often. But it is an excellent example to demonstrate the whole range (and boundaries) of potential signature patterns. The changes of symmetry in the variance allows the use of related statistical tests.

1Data and the Rhizoctonia image have been provided by Dr. Christian Hillnhütter. More detailed information in Hillnhüter et al., 2012, Use of imaging spectroscopy to discriminate symptoms caused by Heterodera schachtii and Rhizoctonia solani on sugar beet,Precision Agric, DOI 10.1007/s11119-011-9237-2
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