Little baraminological research has been conducted on fossil groups, and even less research has considered dinosaurs. In this study, I analyzed a theropod dinosaur group, Tyrannosauroidea, through the use of statistical baraminology. Four cladistic datasets were reanalyzed through baraminic distance correlation (BDC) and multidimensional scaling (MDS). Because many of the supposed intermediary forms are poorly known, they were excluded from the four analyses. In order to further test the baraminic status of Tyrannosauroidea, I performed another analysis of one of the datasets, encompassing more taxa, but with very few characters. Lastly, a subset of the Xu et al. (2012) dataset was analyzed in order to better understand the relationships among the "basal" tyrannosauroids. As a result of these analyses, I arrived at four conclusions. Firstly, there is strong positive BDC correlation and close MDS grouping within the family Tyrannosauridae. Secondly, there is a strong negative BDC correlation and visually distinct gap in the MDS between Tyrannosauridae and the more distant members of the superfamily Tyrannosauroidea and between Tyrannosauridae and non-tyrannosauroid theropod outgroup. Thirdly, there is fairly strong evidence of positive BDC correlation and MDS clustering between Tyrannosauridae, five close members of Tyrannosauroidea (Bistahieversor, Appalachiosaurus, Dryptosaurus, Raptorex, Xiongguanlong), and possibly with the more distant tyrannosauroid Eotyrannus. Fourthly, there is negative BDC correlation and a distinct visual MDS gap between the Tyrannosauridae with some close tyrannosauroids and the more distant tyrannosauroids and outgroup taxa. Based on these results, I determine that Tyrannosauridae is monobaraminic and, along with Bistahieversor, Appalachiosaurus, Dryptosaurus, Raptorex, Xiongguanlong, and possibly Eotyrannus, is holobaraminic with respect to other members of Tyrannosauroidea and all other dinosaurs. The position of Eotyrannus in the biological trajectory of this holobaramin suggests that tyrannosaurs may have originally had smaller skulls and longer arms in proportion to their bodies and three-fingered hands. Because many of the "basal" tyrannosauroids are poorly known, further discoveries of more complete specimens may place them within this holobaramin, or they may provide a link between Tyrannosauridae and other theropods. This article marks the first dinosaur holobaramin defined via statistical baraminology, and the results of this study suggest that the taxa Dinosauria, Saurischia, and Theropoda are polybaraminic.