For sensor networks deployed to monitor and report real events, event source anonymity is an attractive and critical security property, which unfortunately is also very difficult and expensive to achieve. This is not only because adversaries may attack against sensor source privacy through traffic analysis, but also because sensor networks are very limited in resources. As such, a practical tradeoff between security and performance is desirable. In this paper, for the first time we propose the notion of statistically strong source anonymity, under a challenging attack model where a global attacker is able to monitor the traffic in the entire network. We propose a scheme called FitProbRate, which realizes statistically strong source anonymity for sensor networks. We also demonstrate the robustness of our scheme under various statistical tests that might be employed by the attacker to detect real events. Our analysis and simulation results show that our scheme, besides providing source anonymity, can significantly reduce real event reporting latency compared to two baseline schemes.