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Statistics Notes: One and two sided tests of significance

BMJ 1994; 309 doi: (Published 23 July 1994) Cite this as: BMJ 1994;309:248
  1. J M Bland,
  2. D G Bland
  1. Department of Public Health Sciences, St George's Hospital Medical School, London SW 17 ORE Medical Statistics Laboratory, Imperial Cancer Research Fund, London WC2A 3PX.

    In some comparisons - for example, between two means or two proportions - there is a choice between two sided or one sided tests of significance (all comparisons of three or more groups are two sided).

    * This is the eighth in a series of occasional notes on medical statistics.

    When we use a test of significance to compare two groups we usually start with the null hypothesis that there is no difference between the populations from which the data come. If this hypothesis is not true the alternative hypothesis must be true - that there is a difference. Since the null hypothesis specifies no direction for the difference nor does the alternative hypothesis, and so we have a two sided test. In a one sided test the alternative hypothesis does specify a direction - for example, that an active treatment is better than a placebo. This is sometimes justified by saying that we are not interested in the possibility that the active treatment is worse than no treatment. This possibility is still part of …

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