9.2.3.2  The standardized mean difference

The standardized mean difference is used as a summary statistic in meta-analysis when the studies all assess the same outcome but measure it in a variety of ways (for example, all studies measure depression but they use different psychometric scales). In this circumstance it is necessary to standardize the results of the studies to a uniform scale before they can be combined. The standardized mean difference expresses the size of the intervention effect in each study relative to the variability observed in that study. (Again in reality the intervention effect is a difference in means and not a mean of differences.):

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Thus studies for which the difference in means is the same proportion of the standard deviation will have the same SMD, regardless of the actual scales used to make the measurements.

 

However, the method assumes that the differences in standard deviations among studies reflect differences in measurement scales and not real differences in variability among study populations. This assumption may be problematic in some circumstances where we expect real differences in variability between the participants in different studies. For example, where pragmatic and explanatory trials are combined in the same review, pragmatic trials may include a wider range of participants and may consequently have higher standard deviations. The overall intervention effect can also be difficult to interpret as it is reported in units of standard deviation rather than in units of any of the measurement scales used in the review, but in some circumstances it is possible to transform the effect back to the units used in a specific study (see Chapter 12, Section 12.6).

 

The term ‘effect size’ is frequently used in the social sciences, particularly in the context of meta-analysis. Effect sizes typically, though not always, refer to versions of the standardized mean difference. It is recommended that the term ‘standardized mean difference’ be used in Cochrane reviews in preference to ‘effect size’ to avoid confusion with the more general medical use of the latter term as a synonym for ‘intervention effect’ or ‘effect estimate’. The particular definition of standardized mean difference used in Cochrane reviews is the effect size known in social science as Hedges’ (adjusted) g.

 

It should be noted that the SMD method does not correct for differences in the direction of the scale. If some scales increase with disease severity whilst others decrease it is essential to multiply the mean values from one set of studies by –1 (or alternatively to subtract the mean from the maximum possible value for the scale) to ensure that all the scales point in the same direction. Any such adjustment should be described in the statistical methods section of the review. The standard deviation does not need to be modified.