Endgames Statistical Question

Pearson’s correlation coefficient

BMJ 2012; 345 doi: https://doi.org/10.1136/bmj.e4483 (Published 04 July 2012) Cite this as: BMJ 2012;345:e4483
  1. Philip Sedgwick, senior lecturer in medical statistics
  1. 1Centre for Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
  1. p.sedgwick{at}sgul.ac.uk

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 29%. A significant correlation existed between the number of psychiatric NHS beds each year and the combined number of involuntary admissions for mental disorders to NHS and private facilities under the Mental Health Act 1983 (Pearson correlation coefficient r=−0.94 (P<0.001)).

Which of the following statements, if any, are true?

  • a) The Pearson correlation coefficient provides a measure of the strength of linear association between two variables.

  • b) The number of NHS psychiatric beds each year was negatively correlated with the number of involuntary admissions for mental disorders per annum.

  • c) The significance test for the Pearson correlation coefficient is non-parametric.

  • d) It can be deduced that the decrease in the number of NHS psychiatric beds was caused by a rise in the number of involuntary admissions for mental disorders each year.

Answers

Statements a and b are true, while c and d are false.

The Pearson correlation coefficient measures the strength of linear association between two variables (statement a is true)—in the …

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