Standardized mean difference

The most appropriate standardized mean difference (SMD) from a cross-over trial divides the mean difference by the standard deviation of measurements (and not by the standard deviation of the differences). A SMD can be calculated by pooled intervention-specific standard deviations as follows:




A correlation coefficient is required for the standard error of the SMD:


Alternatively, the SMD can be calculated from the MD and its standard error, using an imputed correlation:

In this case, the imputed correlation impacts on the magnitude of the SMD effect estimate itself (rather than just on the standard error, as is the case for MD analyses in Section Imputed correlations should therefore be used with great caution for estimation of SMDs.