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Table 1 The network Q statistics and the degrees of freedom of their corresponding chi-squared distribution

From: A graphical tool for locating inconsistency in network meta-analyses

Null hypothesis Q statistic Degrees of freedom
Homogeneity in the whole network Q net d f Q net := s S ( N s 1 ) T
Homogeneity within designs Q het d f Q het := d = 1 D d f Q d het
Homogeneity within design d Q d het d f Q d het := s S d ( N s 1 ) N d +1
Consistency between designs Q inc d f Q inc := d = 1 D ( N d 1 ) T
Consistency between designs after Q ( d ) inc d f Q ( d ) inc :=d f Q inc N d +1
detaching the effect of design d   
  1. In a network with T+1 treatments and a set of studies S, d=1,…,D designs are observed. The set of studies with design d is given by S d . The numbers of treatments in study s and in design d are given by N s and N d respectively.