Nemaplot hyperspectral data analysis and population modellingEvaluation reinvented


Testing for differences between two mean spectra and results:

We have chosen one top and bottom end example to demonstrate the analysis of a two means comparison problem, somehow equivalent to a t-test (if you ignore the assumptions of a t-test). The graphs show the mean reflectance signatures of both control and treatment with the 95% confidence bands in the domain up to 1050 nm.

Spectral example for highly significant differences
Spectral example for no differences (n.s.)
Comparison of hyperspectral signatures with confidence bands Comparison of hyperspectral signatures with confidence bands

After model fitting and discriminant analysis the result contains several statistical parameter (showing simultaneously in the same direction in most of the cases), which allow the interpretation of the trial. The interpretation must not be overstressed, the question in this case:
Is there a treatment effect compared to the control?
Nothing more and nothing less.

The table summarises the two examples depicted in the graphs above in terms of their gained statistical parameters, how these parameter changes with the situation, and what kind of interpretation exist.
Statistical parameter Different Explanation No difference Explanation
c2 P=0.000 The significance of the discriminant functions gives a first hint of treatment effects. As smaller the probability value p, as larger the differences p=0.924 The usual boundaries are used: p>0.05 or better p>0.01, non significant (n.s.)
Canonical correlation r=0.93 As in the classical correlation we can use the common separation:
  • 0-0.3: no difference; (ns)
  • 0.3-0.8: poor to medium differences, significant difference;
  • 0.8 to 1.0, highly significant different; (***)
r=0.193 no correlation, not significant
Canonical distance 4.9 The most interesting parameter: Based on an arbitrary, dimensionless scale we can quantify the comparison, the value describes the intensity of the treatment effect. 0.4 Distance is less than 1, obvious no treatment effect.
Classification 95% Very high percentage of correct classification, the data distribution indicates a large difference and a clear distinction. 50% The bottom end of any classification; the result indicates randomness; no distinction possible; in fact no treatment was induced in this data set.

ANOVA of the mean comparison

    Difference No difference Explanation
Parameter Model label F-value p-value F-value p-value Meaning of model parameters Slight cut backs must be made in the interpretation of the ANOVA table, as the internal correlation of the model parameter is not taken into account in the ANOVA, therefore it should be used for orientation only. The standard boundary of 5% for the statistical decision is not valid here. We assume p-values <0.01  (or < 1%) are significant, certainty exists with p-values <0.000. The more the spectra differ, the more model parameters are significant different. In case of significances, the size of the F-value depicts how much of the distinction is affected by this parameter and in which domain of the spectra treatment effects are largest. The model exponents (not shown in the graph) are describing the slopes of the amplitudes, but should not get too much weight alone in the interpretation of the results.
A A 0.821 0.371 0.097 0.756
B1 B1 25.717 0.000 0.000 0.994
nma1 AC1 0.408 0.527 0.250 0.617
nmb1 BC1 39.282 0.000 0.41 0.840
a1 AL1 4.134 0.049 0.451 0.503
b1 BE1 3.060 0.089 0.474 0.492
B2 B2 16.369 0.000 0.008 0.930
nma2 AC2 62.845 0.000 0.011 0.920
nmb2 BC2 37.501 0.000 0.003 0.054
a2 AL2 37.778 0.000 0.041 0.839
b2 BE2 4.856 0.034 0.198 0.657
B2 B3 16.869 0.000 0.003 0.955
nma3 AC3 50.742 0.000 0.343 0.558
a3 AL3 15.492 0.000 0.375 0.541

Summary classification

Distribution of classification (discriminant scores), different Distribution of classification (discriminant scores), no difference
Distribution of the classification istribution of the discriminant scores
Demonstration of the variance found in the spectral measurements, also affected by the individuality of the specific single plant. No overlapping exits in the distribution, but an obvious discrimination of the treatment. Obvious overlapping of the distance classes, no distinction of the spectra, variance larger than the mean canonical distance.

A typical outcome of an experiment

On average data will be most likely in between the two extremes as the following example shows; the following spectra were recorded with given variance

Spectra Distribution of discriminant scores
Durchschnittlicher Spektralvergleich Klassifikationsverteilung

Statistical parameter Value Explanation
c2 P=0.000 Discriminant function is significant indicating a significant difference between treatment and control.
Canonical correlation 0.80 Correlation is high on a scale from 0 to +1, also for this parameter, the difference is obvious.
Canonical distance 2.74 The averaged distance is relatively high, overlapping classification scores are due to the natural variance by the individual plant.
Classification 90% Extremely high for spectra apparently not differing from each other.

Model label F-value p-value ANOVA table and explanation
A 0.331 0.567 By chance, the given example demonstrate the limits of the ANOVA. Numerous parameter are below a p-Value of 5%, but by the criteria to use here only parameter Bcrit2 and Acrit3 account for the differences caused by the treatment. Both parameter describes the amplitude in the higher wavelength domains. The treatment effect leads to changes in the structural tissue of the plant.
B1 0.072 0.790
AC1 2.858 0.095
BC1 4.041 0.048
AL1 4.962 0.029
BE1 6.362 0.014
B2 4.389 0.039
AC2 0.004 0.951
BC2 7.248 0.009
AL2 8.362 0.005
BE2 0.099 0.754
B3 4.478 0.038
AC3 30.832 0.000
AL3 1.173 0.282


The common example shown here demonstrates how reflectance data are used to discriminate simple treatment effects out of a cloud of information and how to confirm your findings in statistical terms. To address the individuality of your experiment, just the hyperspectral signature data are needed.

hyperspektrale Fleischanalyse Back to analysis Continue to time series analysis time series of hyperspectral reflectance data


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