Recent studies have demonstrated that analysis of laboratory-quality voice recordings can be used to accurately differentiate people diagnosed with Parkinsons disease (PD) from healthy controls (HC). These findings could help facilitate the development of remote screening and monitoring tools for PD. In this study, we analyzed 2759 telephone-quality voice recordings from 1483 PD and 15321 recordings from 8300 HC participants. To account for variations in phonetic backgrounds, we acquired data from seven countries. We developed a statistical framework for analyzing voice, whereby we computed 307 dysphonia measures that quantify different properties of voice impairment, such as, breathiness, roughness, monopitch, hoarse voice quality, and exaggerated vocal tremor. We used feature selection algorithms to identify robust parsimonious feature subsets, which were used in combination with a Random Forests (RF) classifier to accurately distinguish PD from HC. The best 10-fold cross-validation performance was obtained using Gram-Schmidt Orthogonalization (GSO) and RF, leading to mean sensitivity of 64.90% (standard deviation, SD 2.90%) and mean specificity of 67.96% (SD 2.90%). This large-scale study is a step forward towards assessing the development of a reliable, cost-effective and practical clinical decision support tool for screening the population at large for PD using telephone-quality voice.