In the literature of spectral unmixing (SU), particularly for remote sensing applications, there are claims that both geometric and statistical techniques using independency as cost functions1-4, are very applicable for analysing hyperspectral imagery. These claims are vigorously examined and verified in this paper, using sets of simulated and real data. The objective is to study how effective these two SU approaches are with respected to the modality and independency of the source data. The data sets are carefully designed such that only one parameter is varied at a time. The 'goodness' of the unmixed result is judged by using the well-known Amari index (AI), together with a 3D visualisation of the deduced simplex in eigenvector space. A total of seven different algorithms, of which one is geometric and the others are statistically independent based have been studied. Two of the statistical algorithms use non-negative constraint of modelling errors (NMF & NNICA) as cost functions and the other four employ the independent component analysis (ICA) principle to minimise mutual information (MI) as the objective function. The result has shown that, the ICA based statistical technique is very effective to find the correct endmember (EM) even for the highly intermixed imagery, provided that the sources are completely independent. Modality of the data source is found to only have a second order impact on the unmixing capabilities of ICA based algorithms. All ICA based algorithms are seen to fail when the MI of sources are above 1, and the NMF type of algorithms are found even more sensitive to the dependency of sources. Typical independency of species found in the natural environment is in the range of 15-30. This indicates that, conventional statistical ICA and matrix factorisation (MF) techniques, are really not very suitable for the spectral unmixing of hyperspectral (HSI) data. Future work is proposed to investigate the idea of a dependent component clustering technique, a fused geometric and statistical approach, and couple these with a modification of the conventional ICA based algorithms to model the independency of the mixing, rather than the sources. This work formulates part of the research programme supported by the EMRS DTC established by the UK MOD.