This paper makes an outline case for the need for a low-cost, easy to administer method for detecting dementia within the growing at risk population. It proposes two methods for electroencephalogram (EEG) analysis for detecting dementia that could fulfil such a need. The paper describes a fractal dimension-based method for analyzing the EEG waveforms of subjects with dementia and reports on an assessment which demonstrates that an appropriate fractal dimension measure could achieve 67% sensitivity to probable Alzheimer's disease (as suggested by clinical psychometric testing and EEG findings) with a specificity of 99.9%. An alternative method based on the probability density function of the zero-crossing intervals is shown to achieve 78% sensitivity to probable Alzheimer's disease and an estimated sensitivity to probable Vascular (or mixed) dementia of 35% (as suggested by clinical psychometric testing and EEG findings) with a specificity of 99.9%. This compares well with other studies, reported by the American Academy of Neurology, which typically provide a sensitivity of 81% and specificity of 70%. The EEG recordings used to assess these methods included artefacts and had no a priori selection of elements "suitable for analysis." This approach gives a good prediction of the usefulness of the methods, as they would be used in practice. A total of 39 patients (30 probable Alzheimer's Disease, six Vascular Dementia and three mixed dementia) and 42 healthy volunteers were involved in the study. However, although results from the preliminary evaluation of the methods are promising, there is a need for a more extensive study to validate the methods using EEGs from a larger and more varied patient cohorts with neuroimaging results, to exclude other causes and cognitive scores to correlate results with severity of cognitive status.