Engaged in medical research. Has applied the statistical method to the elucidation of many problems of physiology, pathology, hygiene and epidemiology. Is the author, or joint author, of more than sixty papers dealing with these applications, including important contributions to the experimental study of epidemiology (Journ Hyg, 24, 1925, Greenwood and Topley; ibid, 25, 1926, Greenwood, Newbold, Topley and Wilson). Has done much to encourage and develop the use of modern statistical methods by medical laboratory investigators, and, as Chairman of the Medical Research Council's Statistical Committee, to secure the adequate planning and execution of field investigations.
Greenwood produced a large body of research, was the first holder of important positions in modern medical statistics and wrote extensively on the history of his subject, but as Austin Bradford Hill wrote in his obituary, "in the future, it may well indeed seem that one of his greatest contributions, if not the greatest, lay merely in his outlook, in his statistical approach to medicine, then a new approach and one long regarded with suspicion. And he fought this fight continuously and honestly—for logic for accuracy, for ‘little sums.’" A statistical method invented by Major Greenwood in a statistical study of infectious diseases  is still used in present day research. The Greenwood statistic was used to discover that there is some kind of order in the placement of genes on the chromosomes of living things  and this inspired a new look at epigenetics, which is now considered to be equally as important as genetics in how living organisms develop and evolve.
M. Greenwood (1904) "A First Study of the Weight, Variability, and Correlation of the Human Viscera, with Special Reference to the Healthy and Diseased Heart", Biometrika, 3, 63-83.
Major Greenwood and G. Udny Yule (1915) "The Statistics of Anti-Typhoid and Anti-Cholera Inoculations, and the Interpretation of such Statistics in General", Proceedings of the Royal Society of Medicine (Epidemiology), 8, 113-190.
Major Greenwood and G. Udny Yule (1920), "An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents". Journal of the Royal Statistical Society, 83: 255-279.
Edgar L. Collis and Major Greenwood The health of the industrial worker. 1921
Major Greenwood Epidemics and crowd-diseases: an introduction to the study of epidemiology. 1935
Major Greenwood Medical statistics from Graunt to Farr: the Fitzpatrick lectures for the years 1941 and 1943. 1948