This thesis reports on the foundation, establishment, development, and initial outcomes of the large-scale pulsar radio emission statistics survey (PRESS), which was initiated and carried out during this PhD project. The research started by developing and testing novel methods of analysing single-pulse polarisation fluctuation, based on the theory developed by van Straten (2009) and van Straten and Tiburzi (2017). For this pioneering effort, we used an existing set of single-pulse polarisation observations recorded at the Arecibo radio telescope (Hankins & Rankin, 2010). By analysing the covariances between the Stokes parameters in these archival data, we discovered several rare polarisation phenomena.

In particular, the Arecibo data included a highly sensitive observation of the first- discovered pulsar, PSR B1919+21 (also known as PSR J1921+2153), which allowed us to perform a direct comparison between our statistical approach and more traditional methods of analysis. For example, principal component analysis of the matrix of covariances between the Stokes parameters led to the discovery of an unexpected oblate spheroidal distribution of the polarisation vector. This was confirmed using a scatter plot in the Poincaré sphere, which revealed a toroidal distribution of polarisation vectors centered near the origin of the Poincaré sphere. Further temporal and spectral analysis of the polarization fluctuations led us to discover that the polarisation vectors cycle around the toroidal axis of revolution synchronously with the drifting sub-pulse modulation of the total intensity, an effect that has been observed in only one other study (Edwards, 2004).

Prior to launching the observation campaign for PRESS, we experimentally verified a novel equation that describes sensitivity to the variance of modulated radio emission using single pulse observations of PSR J0437-4715 (Osłowski et al., 2014). After a brief description of the observing campaign that was carried out using Murriyang, the 64-m Parkes radio telescope, we present an overview of the current state of the PRESS data processing pipeline, including encountered challenges and solutions implemented during pipeline development. This part of the thesis primarily describes our efforts to validate the quality of the outputs produced by the data processing pipeline and the challenges presented by Radio Frequency Interference.

Finally, we report on the preliminary results of a single-pulse statistical analysis of PRESS observations of PSR J1921+2153. The techniques, tools, and data presented in this thesis create new opportunities for future single pulse studies of radio pulsar emission.