Alzheimer's disease (AD) and other forms of dementia are one of the major public health and social challenges of our time because of the large number of people affected. Early diagnosis is important for patients and their families to get maximum benefits from access to health and social care services and to plan for the future. EEG provides useful insight into brain functions and can play a useful role as a first line of decision-support tool for early detection and diagnosis of dementia. It is non-invasive, low-cost and has a high temporal resolution. The functions of brain cells are affected by damage caused by dementia and this in turn causes changes in the features of the EEG. Information theoretic methods have emerged as a potentially useful way to quantify changes in the EEG as biomarkers of dementia. Tsallis entropy has been shown to be one of the most promising information theoretic methods for quantifying changes in the EEG. In this paper, we develop the approach further. This has yielded an enhanced performance compared to existing approaches.