This study considered all articles published in six Public Library of Science (PLOS) journals in 2012 and Web of Science citations for these articles as of May 2015. A total of 2,406 articles were analyzed to examine the relationships between Altmetric Attention Scores (AAS) and Web of Science citations. The AAS for an article, provided by Altmetric aggregates activities surrounding research outputs in social media (news outlet mentions, tweets, blogs, Wikipedia, etc.). Spearman correlation testing was done on all articles and articles with AAS. Further analysis compared the stratified datasets based on percentile ranks of AAS: top 50%, top 25%, top 10%, and top 1%. Comparisons across the six journals provided additional insights. The results show significant positive correlations between AAS and citations with varied strength for all articles and articles with AAS (or social media mentions), as well as for normalized AAS in the top 50%, top 25%, top 10%, and top 1% datasets. Four of the six PLOS journals, Genetics, Pathogens, Computational Biology, and Neglected Tropical Diseases, show significant positive correlations across all datasets. However, for the two journals with high impact factors, PLOS Biology and Medicine, the results are unexpected: the Medicine articles showed no significant correlations but the Biology articles tested positive for correlations with the whole dataset and the set with AAS. Both journals published substantially fewer articles than the other four journals. Further research to validate the AAS algorithm, adjust the weighting scheme, and include appropriate social media sources is needed to understand the potential uses and meaning of AAS in different contexts and its relationship to other metrics.