Wireless sensor networks are composed of distributed sensors that can be used for signal detection or classification. The likelihood functions of the hypotheses are often not known in advance, and decision rules have to be learned via supervised learning. A specific learning algorithm is Fisher discriminant analysis (FDA), the classification accuracy of which has been previously studied in the context of wireless sensor networks. Previous work, however, does not take into account the communication protocol or battery lifetime; in this paper we extend existing studies by proposing a model that captures the relationship between battery lifetime and classification accuracy. To do so, we combine the FDA with a model that captures the dynamics of the carrier-sense multiple-access (CSMA) algorithm, the random-access algorithm used to regulate communications in sensor networks. This allows us to study the interaction between the classification accuracy, battery lifetime and effort put towards learning, as well as the impact of the back-off rates of CSMA on the accuracy. We characterize the tradeoff between the length of the training stage and accuracy, and show that accuracy is non-monotone in the back-off rate due to changes in the training sample size and overfitting. Copyright 2013 ACM.