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Measuring packet delay and packet loss through dedicated test packet streams in computer networks allows for the assessment of Quality of Service on the path the probes traverse. For this reason, active IP performance measurements have been carried out in X-WiN, Germany's National Research and Educational Network, and GEANT2, its European counterpart, by the WiN-Labor Group of the University of Erlangen-Nuremberg for many years. This paper provides an overview of how network measurements can be interpreted using a variety of statistical concepts in order to gain insight into the state of monitored connections. The focus here is set on the analysis of One-Way Delay (OWD); the approach demonstrates how OWD can be used for the identification of network congestions and can serve as a basis for network alert systems by statistically categorizing changes in the performance metric.