Morans

Morans is a surname form that may refer to people and families bearing the name Morans, a variant of Moran with Irish origins. The name Moran comes from Gaelic Ó Móráin or Mórán, and Morans is encountered in Ireland and among communities descended from Irish emigrants. The spelling Morans may occur in English-language contexts as a family name.

Moran's I is a statistic used to measure spatial autocorrelation, i.e., the degree to which similar values occur near each other in geographic space. It was introduced by statistician Patrick A. Moran. The calculation uses an observations vector x and a spatial weights matrix W, with I = (N/W) times the sum over all i and j of w_ij times (x_i − x_bar)(x_j − x_bar), divided by the sum over i of (x_i − x_bar) squared. Values typically range from -1 to +1; positive values indicate clustering of similar values, negative values indicate dispersion, and values near zero suggest spatial randomness. Moran's I is widely used in geography, ecology, epidemiology, and related fields, often with significance tested via permutation or randomization. Univariate Moran's I analyzes a single attribute across locations, while a related form, bivariate Moran's I, assesses spatial association between two attributes.

Beyond Moran's I, the term Morans can appear in discussions of related methods, such as Moran's scatterplot (a diagnostic plot) and Moran's eigenvector maps (MEM), which are used to model spatial structure in ecological analyses. The precise meaning of Morans depends on the context and discipline, but Moran's I remains the most common statistical reference.