Intended for healthcare professionals

Endgames Statistical Question

Log transformation of data

BMJ 2012; 345 doi: (Published 08 October 2012) Cite this as: BMJ 2012;345:e6727
  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}

Researchers evaluated the effectiveness of early abdominopelvic computed tomography in patients with acute abdominal pain of unknown cause. A randomised controlled trial study design was used. The intervention was early computed tomography (within 24 hours of admission). The control treatment was standard practice (radiological investigations as indicated). In total, 55 patients were randomised to early computed tomography and 55 to control treatment.1

The main outcome measures included length of hospital stay. The distribution of length of hospital stay was positively skewed. The logarithm function was used to transform the observations, and the Student’s t test was then used to compare the treatment groups. The length of hospital stay for the standard practice group was on average 1.1 days longer than that in the early computed tomography group (geometric mean 6.4 days (range 1 to 60) versus 5.3 days (1 to 31). The ratio of geometric means (standard treatment versus early computed tomography) was 1.21 (95% confidence interval 0.92 to 1.56).

The overall conclusions of the study were that early abdominopelvic computed tomography for acute abdominal pain may reduce length of hospital stay and mortality. Furthermore, it could also identify unforeseen conditions and potentially serious complications.

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

  • a) The purpose of the logarithm transformation of length of hospital stay was to achieve a normal distribution.

  • b) In each treatment group, the geometric mean of length of hospital stay was larger than the arithmetic mean.

  • c) The standard practice group spent on average 21% longer in hospital than the early computed tomography group.

  • d) The difference between treatments in length of hospital stay …

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