Sometimes it is desirable to combine two reported subgroups into a single group. This might be the case, for example, if a study presents sample sizes, means and standard deviations separately for males and females in each of the intervention groups. The formulae in Table 7.7.a can be used to combine numbers into a single sample size, mean and standard deviation for each intervention group (i.e. combining across males and females in this example). Note that the rather complex-looking formula for the SD produces the SD of outcome measurements as if the combined group had never been divided into two. An approximation to this standard deviation is obtained by using the usual pooled standard deviation, which provides a slight underestimate of the desired standard deviation.
These formulae are also appropriate for use in studies that compare more than two interventions, to combine two intervention groups into a single intervention group (see Chapter 16, Section 16.5). For example, ‘Group 1’ and ‘Group 2’ might refer to two alternative variants of an intervention to which participants were randomized.
If there are more than two groups to combine, the simplest strategy is to apply the above formula sequentially (i.e. combine group 1 and group 2 to create group ‘1+2’, then combine group ‘1+2’ and group 3 to create group ‘1+2+3’, and so on).