There is a vast range of manual activities, such as writing, for which consistent use of one hand can be observed - for most people it is the right one. But some people do use their left hand for some of these activities, their right for others. It was the 1970s turn in research to identify this third group of "mixed-handers" - even with inventories of as few as 10 or so activities. My contribution - in the 1980s - was to subject two British inventories to principal components analysis and find only one component passing the usual requirements for further analysis. On subsequent factor analysis stipulating no more than a single factor, this factor accounted for a very great deal of the variance in the correlation matrices and might as well be called Handedness (Cortex 22, 325-6, International Journal of Clinical Neuropsychology 11). I have also compared these inventories (Edinburgh and Annett's) with one another regarding their utility as clinical and research tools (Neuropsychology 5). 

Why are researchers so interested in this topic?  Mainly, in my view, because of the different aphasiological patterns (speech disorders) of left-handed and right-handed brain-damaged patients often reported by studies comparing them. Traditionally, this was explained by a concept of "cerebral dominance", the normal (and right-handers') dominance being of the left cerebrum for language, but not uncommonly in left-handers belonging to the right cerebrum/hemisphere. Post-War the evidence for this moved on beyond passive study of people with unilateral (one-sided) cerebral lesions to use temporary anaesthetization of the single hemisphere. Intriguingly, this work also identified, particularly among left-handed patients, some who suffered a mild transient aphasia from anaesthetization (with sodium amytal) of either cerebrum. Could this be a parallel to mixed-handedness?

It is no surprise that there have been recurrent reports of a small correlation even in neurologically intact people between their handedness and their cognitive attainment. I was myself the author of one of them (measuring scholastic performance for a study in the Journal of Genetic Psychology 148). And it is also my impression that left-handedness has long been used as a "soft" indicator of neurological damage (possibly "minimal"). More recently a left-ear advantage in dichotic listening to speech has been taken as a possible sign of atypical "cerebral dominance" / "hemispheric asymmetry". That sort of advantage is likely to be correlated with telephoning and "telephone ear" in turn with handedness (see my article available here).