Correction methods for ties in rank correlations

Equal values are common when rank methods are applied to rounded data or data consisting solely of small integers. A popular technique for resolving ties in rank correlation is the mid-rank method: the mean of the rankings remains unaltered, but the variance is reduced and modified according to the number and location of ties. Although other methods for breaking ties were proposed in the literature as early as 1939, no such procedure has gained such wide acceptance as mid-ranks. This research analyses various techniques for assigning ranks to tied values, with two objectives: (1) to enable the computation of rank correlation coefficients, such as those of Spearman, Kendall and Gini, by using the usual definition applied in the absence of ties, and (2) to determine whether it really makes a difference which of the various techniques is selected and, if so, which technique is most appropriate for a given application.     

A sustainable urban regeneration project to protect biodiversity

Urban Ecosystems - The sustainable urban redevelopment project to protect biodiversity was developed to regenerate the external spaces of an ancient rural farmhouse, Villa Framarino, in the...