Deep neural networks are vulnerable to adversarial examples. Prior defenses attempted to make deep networks more robust by either changing the network architecture or augmenting the training set with adversarial examples, but both have inherent limitations. Motivated by recent research that shows outliers in the training set have a high negative influence on the trained model, we studied the relationship between model robustness and the quality of the training set. We first show that outliers give the model better generalization ability but weaker robustness. Next, we propose an adversarial example detection framework, in which we design two methods for removing outliers from training set to obtain the sanitized model and then detect adversarial example by calculating the difference of outputs between the original and the sanitized model. We evaluated the framework on both MNIST and SVHN. Based on the difference measured by Kullback-Leibler divergence, we could detect adversarial examples with accuracy between 94.67% to 99.89%.