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Education And Debate

Statistics Notes: Comparing several groups using analysis of variance

BMJ 1996; 312 doi: (Published 08 June 1996) Cite this as: BMJ 1996;312:1472
  1. Douglas G Altman, heada,
  2. J Martin Bland, professor of medical statisticsb
  1. a IRCF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF
  2. b Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
  1. Correspondence to: Mr Altman.

    Many studies, including most controlled clinical trials, contrast data from two different groups of subjects. Observations which are measurements are often analysed by the t test, a method which assumes that the data in the different groups come from populations where the observations have a normal distribution and the same variances (or standard deviations). While the t test is well known, many researchers seem unaware of the correct method for comparing three or more groups. For example, table 1 shows measurements of galactose binding for three groups of patients. A common error is to compare each pair of groups using separate two sample t tests1 with the consequent problem of multiple testing.2 The correct approach is to use one way analysis of variance (also called ANOVA), which is based on the same assumptions as the t test. We compare the groups to evaluate whether there is evidence that the means of the populations differ. Why then is the method called analysis of variance?

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    Table 1

    Measurements …

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