Pre-training language models (LMs) on large-scale unlabeled text data makes the model much easier to achieve exceptional downstream performance than their counterparts directly trained on the downstream tasks. In this work, we study what specific traits in the pre-training data, other than the semantics, make a pre-trained LM superior to their counterparts trained from scratch on downstream tasks. We propose to use artificially constructed datasets as the pre-training data to exclude the effect of semantics, and further control what characteristics the pre-training corpora have. By fine-tuning the pre-trained models on GLUE benchmark, we can learn how beneficial it is to transfer the knowledge from the model trained on the dataset possessing that specific trait. We define and discuss three different characteristics in the artificial dataset: 1) matching the token's uni-gram or bi-gram distribution between pre-training and downstream fine-tuning, 2) the presence of the explicit dependencies among the tokens in a sequence, 3) the length of the implicit dependencies among the tokens in a sequence. Our experiments show that the explicit dependencies in the sequences of the pre-training data are critical to the downstream performance. Our results also reveal that models achieve better downstream performance when pre-trained on a dataset with a longer range of implicit dependencies. Based on our analysis, we find that models pre-trained with artificial datasets are prone to learn spurious correlation in downstream tasks. Our work reveals that even if the LMs are not pre-trained on natural language, they still gain transferability on certain human language downstream tasks once the LMs learn to model the token dependencies in the sequences. This result helps us understand the exceptional transferability of pre-trained LMs.