What do coal geochemistry statistics really mean?

Modes of occurrence of elements in coal have been widely investigated using different methods, including statistical methods, which, however, in some cases resulted in misleading interpretations. In order to verify this potential problem and find an effective solution, we selected a data set which contained comprehensive analyses of 27 coal bench samples with ash yields ranging from 3.66% to 46.56% in a single Paleozoic coal seam from the Haerwusu Surface Mine, Inner Mongolia, China. The correlation coefficients between the elemental concentrations versus ash yields were progressively calculated based on variations of ash yields (from the lowest to the highest). The elements were classified using k-means clustering algorithm and the Goldschmidt's geochemical classification. The distinct break of ash yields of -9%, in this case, has been determined for different modes of occurrence of elements in coals with ash yields lower and higher than this break. However, using traditional statistical methods for coal geochemistry analysis, i.e., using the full dataset without separating ash yields, it would not be possible to reach the rational interpretations of the elements modes of occurrence and sources but would result in misinterpretations.