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 highest likelihood ratio as our anomalous window, and (c) Monte Carlo Simulations: to ascertain whether this window is truly anomalous and not just a random occurrence we perform hypothesis testing by computing a p-value using Monte Carlo Simulations. We present extensive experimental results in real world accident datasets for various highways with known issues(code and data available from [27], [21]). Our results show that our approach indeed is effective in identifying anomalous traffic accident windows along multiple intersecting highways.