Endgames Statistical Question

The normal distribution

BMJ 2012; 345 doi: https://doi.org/10.1136/bmj.e6533 (Published 28 September 2012) Cite this as: BMJ 2012;345:e6533
  1. Philip Sedgwick, reader in medical statistics and medical education
  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 whether antidepressant drug prescribing and referrals to specialist services for depression by general practitioners were associated with patients’ scores on depression severity questionnaires measured at the start of treatment. Anonymised data from the medical records of 38 general practices were investigated. The nine item patient health questionnaire (PHQ-9) was used in 1658 patients and the depression subscale of the hospital anxiety and depression scale (HADS) was used in 548 patients.1

The distribution of HADS questionnaire scores for the sample was approximately normal, whereas the PHQ-9 scores were negatively skewed. The mean PHQ-9 score was 15.5 (standard deviation 6.0) and the mean HADS score was 11.1 (4.6). It was reported that patients with higher depression severity scores were more likely to receive prescriptions for antidepressants and be referred to specialist services. However, other factors were independently associated with treatment and referral, including patient age and concurrent physical illness and geographical area.

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

  • a) The normal distribution approximated by the HADS scores can be uniquely described by the sample mean and standard deviation

  • b) The normal distribution approximated by the HADS scores is symmetrical about the sample mean value …

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