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 ttest (if you ignore the assumptions of a ttest). The graphs show the mean reflectance signatures of both control and treatment with the 95% confidence bands in the domain up to 1050 nm.Visualisation: Spectral example for highly significant differences 
Visualisation: Spectral example for no differences (n.s.) 
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 
c^{2}  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:

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  Fvalue  pvalue  Fvalue  pvalue  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 pvalues <0.01 (or < 1%) are significant, certainty exists with pvalues <0.000. The more the spectra differ, the more model parameters are significant different. In case of significances, the size of the Fvalue 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  
B_{1}  B1  25.717  0.000  0.000  0.994  
nm_{a1}  AC1  0.408  0.527  0.250  0.617  
nm_{b1}  BC1  39.282  0.000  0.41  0.840  
a_{1}  AL1  4.134  0.049  0.451  0.503  
b_{1}  BE1  3.060  0.089  0.474  0.492  
B_{2}  B2  16.369  0.000  0.008  0.930  
nm_{a2}  AC2  62.845  0.000  0.011  0.920  
nm_{b2}  BC2  37.501  0.000  0.003  0.054  
a_{2}  AL2  37.778  0.000  0.041  0.839  
b_{2}  BE2  4.856  0.034  0.198  0.657  
B_{2}  B3  16.869  0.000  0.003  0.955  
nm_{a3}  AC3  50.742  0.000  0.343  0.558  
a_{3}  AL3  15.492  0.000  0.375  0.541 
Summary classification  
Distribution of classification (discriminant scores), different  Distribution of classification (discriminant scores), no difference 
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 
Statistical parameter  Value  Explanation 
c^{2}  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  Fvalue  pvalue  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 pValue 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 