Being a promising technology which is envisioned to pervade numerous aspects of human life, wireless sensor networks are attracting remarkable attention in research community. The typical wireless sensors are small low-power, resource-constrained devices subject to functional failures which could be due to power loss or even malicious attacks on the devices. As the projected applications for wireless sensor networks range from smart applications such as traffic monitoring to critical military applications such as measuring levels of gas concentration in battle fields, security in sensor networks becomes a prime concern. In sensitive applications, it becomes imperative to continuously monitor the transient state of the system rather than steady state observations and take requisite preventive and corrective actions, if necessary. Also, the network is prone to attack by adversaries who intend to disrupt the functioning of the system by compromising the sensor nodes and injecting false data into the network. So it is important to shield the sensor network from false data injection attacks. Through this work, we prove that in the presence of adversaries, it would be difficult to correctly observe the transient phenomenon if sensors report just their readings. We develop a novel robust statistical framework to monitor correctly the transient phenomenon while limiting the impact of false data injection. In this framework, each sensor does a lightweight computation and reports a statistical digest in addition to the current sensed reading. Through a series of carefully-designed inter-sensor statistical tests on both the readings and digests, we are able to achieve our goal of preserving the transient phenomenon. We show a concrete realization of our statistical framework by developing a secure statistical scheme, called SSTF, to effectively monitor the transient phenomenon while being immune to false data injection attacks. SSTF is a two-tier system and the kernel of SSTF is our statistical framework, which is employed atop an enhanced version of the IHHAS security scheme. We present detailed theoretical analysis and in-depth simulation results to demonstrate the effectiveness of SSTF.