Pearson's correlation coefficient

Researchers investigated the relation between the number of involuntary admissions (detentions) for mental disorders a year under the Mental Health Act 1983 and the number of NHS psychiatric beds each year in England. They used hospital episode statistics from 1996 to 2006 in a retrospective analysis. For each year they obtained the number of available NHS psychiatric beds—defined as those beds for patients with mental disorders or learning disabilities—and the number of involuntary admissions for mental disorders in NHS hospital and private facilities combined.1 It was reported that the number of NHS psychiatric beds fell in each successive year and that overall from 1996 to 2006 the number had decreased by…