As Run 2 of the LHC completes, a vast set of particle collision data has been recorded by the experimental collaborations on the ring. This has enabled the collaborations to perform many measurements of fiducial particle collision properties, which have been found to be in good agreement with predictions from the Standard Model of particle physics. This collected data has also been used to perform many searches for a variety hypothesised extensions to the Standard Model, which have thus far not observed any significant sign of new physics. In this thesis contributions to the precision measurement program within the ATLAS collaboration at the LHC are presented. These contributions are primarily made to the measurement of detector corrected observables sensitive to large imbalances of momentum observed in the transverse plane. Additionally the opportunity of using such precision fiducial measurements to understand the nature of physics beyond the Standard Model is explored. This is found to give rise to interesting, competitive and complementary information to that derived from the dedicated searches. This work has led to the release of a publicly available program that can be used to automatically confront a hypothesised physics model with precision LHC measurement data. This program is called CONTUR and applications of this to a variety of hypothesised physics models are presented
