It has been noted that ‘Evaluation of health-care interventions rarely concerns a single summary statistic. “Multiplicity” is everywhere’ (Spiegelhalter, Abrams and Myles, 2004, Section 3.17, p. 91). The same is true of most other areas of research. This chapter explores two types of multiplicity, namely
and shows how mixed models can assist the interpretation of the results that they produce.
When several studies have been performed addressing the same question, it is natural to seek to assess the strength of the combined evidence. This situation commonly occurs in medical research, when a number of clinical trials have been conducted to assess the same treatment. None of the trials may provide sufficient evidence on its own to conclude that the treatment is effective, but the combined evidence may nevertheless permit a confident conclusion to be reached. There may be a similar case for the combined analysis of a set of agricultural field experiments, or a set of studies in any other discipline. Such a combined analysis is known as a meta-analysis. Meta-analyses are becoming increasingly common, particularly in medical research, motivated by the need to obtain