Confidence intervals for the standardized effect arising in comparisons of two normal populations

Confidence intervals for a standardized effect are derived after stabilizing the variance of the Welch t-statistic. Simulation studies demonstrate the viability of the resulting intervals for a wide range of parameter values and sample sizes as small as five. The methodology is extended to the combination of results from several studies, so as to obtain a confidence interval for a representative standardized effect for all the studies. The methods are illustrated on a recent meta-analytic study of systolic blood pressure reduction during a weight reducing regime, as well as the classical Mumford data on psychological intervention and hospital length of stay.