As an example, suppose a cross-over trial reports the following data:
Intervention E (sample size 10) |
M_{E} = 7.0, SD_{E} = 2.38 |
Intervention C (sample size 10) |
M_{C} = 6.5, SD_{C} = 2.21 |
The estimate of the mean difference is MD = 7.0 – 6.5 = 0.5. Suppose that a typical standard deviation of differences had been observed from other trials to be 2. Then we can estimate the standard error of MD as
.
The numbers 0.5 and 0.632 may be entered into RevMan as the estimate and standard error of a mean difference, under a generic inverse variance-outcome.
The estimate of the mean difference is again MD = 0.5. Suppose that a correlation coefficient of 0.68 has been imputed. Then we can impute the standard deviation of the differences as:
The standard error of MD is then
.
The numbers 0.5 and 0.583 may be entered into RevMan as the estimate and standard error of a mean difference, under a generic inverse-variance outcome. Correlation coefficients other than 0.68 should be used as part of a sensitivity analysis.
The standardized mean difference can be estimated directly from the data:
.
The standard error is obtained thus:
.
The numbers 0.218 and 0.256 may be entered into RevMan as the estimate and standard error of a standardized mean difference, under a generic inverse-variance outcome.
We could also have obtained the SMD from the MD and its standard error:
The minor discrepancy arises due to the slightly different ways in which the two formulae calculate a pooled standard deviation for the standardizing.