Anomalous windows are the contiguous groupings of data points. In this paper, we propose an approach for discovering anomalous windows using Scan Statistics for Linear Intersecting Paths (SSLIP). A linear path refers to a path represented by a line with a single dimensional spatial coordinate marking an observation point. Our approach for discovering anomalous windows along linear paths comprises of the following distinct steps: (a) Cross Path Discovery: where we identify a subset of intersecting paths to be considered, (b) Anomalous Window Discovery: where we outline three order invariant algorithms, namely SSLIP, Brute Force-SSLIP and Central Brute Force-SSLIP, for the traversal of the cross paths to identify varying size directional windows along the paths. For identifying an anomalous window we compute an unusualness metric, in the form of a likelihood ratio to indicate the degree of unusualness of this window with respect to the rest of the data. We identify the window with the h...