Summary1. Competition theory predicts that community structure may be shaped by resource partitioning between co-occurring species. As such, quantifying the degree of resource partitioning (i.e., niche overlap) is a key component of studies examining community structure and species coexistence. 2. For many organisms, multiple resource axes quantify niche space. Each axis may be described by a different type of data (e.g. categorical, continuous, count or binary data, as well as electivity scores), with different data types requiring different statistical treatments. Therefore, incorporating multiple axes into a single measure of niche space is problematic. 3. Here, we propose general methods for combining multiple niche axes, each characterized by different data types, within a unified analysis of niche overlap. Using appropriate transformations and probability models, we show that each data type can give rise to directly comparable measures of niche overlap, with the overlap statistic between two species defined as the overlapping area between the distributions for each species. 4. Measurements derived from different types of data can be combined into a single unified analysis of niche overlap by averaging over multiple axes. 5. We then describe null model permutation tests that assess statistical differences in niche overlap, which can address questions commonly posed by population ecologists (e.g. do two species occupy different niche space?) and community ecologists (e.g. are multiple species evenly distributed across niche space?). 6. To illustrate the use of these newly devised indices, we use an example from reef fishes that combines ratio, categorical and electivity data, and an example from alpine plants that combines continuous and ratio data. 7. The methods described in this article are relevant to a wide variety of ecological projects, including the investigation of invasive species, relative abundance distributions, global change, species coexistence and evolutionary diversification.