Henry K. Carroll performed an analysis of United States census data in 1912 to assign Roman numerals to various Brethren groups. For example, Brethren III is also known as the Lowe Brethren and the Elberfeld Brethren. Carroll's initial findings listed four sub-groups, identified as Brethren I-IV, but he expanded the number six and then to eight; Arthur Carl Piepkorn expanded the number to ten. Those who have attempted to trace the realignments of the Plymouth Brethren include Ian McDowell and Massimo Introvigne. The complexity of the Brethren's history is evident in charts by McDowell and Ian McKay.