Advanced reading: Introduction and overview about the statistics used in the project:

Meaning of the model parameters — Fig. 1: Labels and domain positions of model parameters

Nemaplot uses the hyperspectral reflectance technology as a non-destructive and non-invasive tool for a fast and early analysis of field, greenhouse or lab experiments and trait recognition of biological objects. We have developed and combined several statistical tools to detect and produce statistical evidence for minor differences in your hyperspectral data. This approach enables rapid analysis of hyperspectral measurements that are themselves fast and easy to conduct, making the whole procedure rapid, effective and affordable. Nemaplot has developed unique methods to detect differences among spectra by a combination of model fitting, parameter estimation procedures and multivariate statistics making otherwise time consuming analysis, simple and effective. The comparison of all parameter estimates (i.e. the whole spectrum) is used to detect treatment effects. The comparison of the parameters allows the setting of statistical decision boundaries and allows the comparison of signatures by the significance of the statistical tests. This patented method is applicable for all spectral reflectance patterns and not reduced for the analysis of vegetation reflectance. We use the complete spectral information. The common use of indices of variable, restricted domain is certainly a no go method.

General double Weibull function

To analyse experiments we introduce a dimensionless scale on the base of discriminant functions. These alternative levels allow us to address the relative differences of the established factor levels. We are delivering a number of statistical parameters which allow the assessment and classification of reflectance data. These statistical parameters are:

Common test parameter, as the c² test and others, determining the discriminating power and group relations, as well the probability testing for group equality (small p-values means unequal groups, caused by treatment impact for example).
Canonical correlation, a measure of the precision of the discriminant functions. We can use the common classes in the interval of 0 to 1: 0-0.3, no correlation, 0.3-0.7, poor to medium association, 0.7 - 1.0 high and very high correlations.
Canonical distances, based on an open dimensionless scale, which provide a quantitative measure and determine the intensities of treatments. As larger the distance, as larger are the differences among groups. With respect to the treatment factor, as larger are the treatment effects.

We are not stressing major differences, the visual distinction is more than obvious in such cases and no test is needed (for example a comparison between a brown and a green leaf), but in the majority of measurements there are apparently no differences in the spectra and treatment effects are not obvious at all. In comparison to the classical statistical analysis on the base of SI units, as kg ha^-1, etc., this method also provides the facility to analyse multi-factorial designs and mean comparison. It is most suitable for high throughput screenings, where treatment related differences (for example due to fertiliser, induced stresses and pesticide treatments or genetically related traits) are recognised at early times and development stages.