Different methods have been suggested for calculating “exact” confidence intervals for a standardized mean difference using the noncentral t distributions. Two methods are provided in Hedges and Olkin (1985, “H”) and Steiger and Fouladi (1997, “S”). Either method can be used with a biased estimator, d, or an unbiased estimator, g, of the population standardized mean difference (methods abbreviated Hd, Hg, Sd, and Sg). Coverages of each method were calculated from theory and estimated from simulations. Average coverages of 95% confidence intervals across a wide range of effect sizes and across sample sizes from 5 to 89 per group were always between 85 and 98% for all methods, and all were between 94 and 96% with sample sizes greater than 40 per group. The best interval estimation was the Sd method, which always produced confidence intervals close to 95% at all effect sizes and sample sizes. The next best was the Hg method, which produced consistent coverages across all effect sizes, although coverage was reduced to 93–94% at sample sizes in the range 5–15. The Hd method was worse with small sample sizes, yielding coverages as low as 86% at n = 5. The Sg method produced widely different coverages as a function of effect size when the sample size was small (93–97%). Researchers using small sample sizes are advised to use either the Steiger & Fouladi method with d or the Hedges & Olkin method with g as an interval estimation method.

已经建议使用不同的方法来计算使用非中心t分布的标准化平均差的“精确”置信区间。Hedges 和 Olkin（1985，“H”）和 Steiger 和 Fouladi（1997，“S”）提供了两种方法。这两种方法都可以与总体标准化平均差的有偏估计量d或无偏估计量g 一起使用（方法缩写为 H d、H g、S d和 S g）。每种方法的覆盖率都是根据理论计算的，并根据模拟进行估计。对于所有方法，在各种效应量和每组 5 到 89 个样本量之间的 95% 置信区间的平均覆盖率始终在 85% 到 98% 之间，并且所有方法都在 94% 到 96% 之间，样本量大于 40%团体。最好的区间估计是 S d方法，它在所有效应量和样本量下总是产生接近 95% 的置信区间。其次是 H g方法，它在所有效应量中产生一致的覆盖率，尽管覆盖率在 5-15 范围内的样本量中降低到 93-94%。H d方法在样本量较小的情况下效果更差，在n处的覆盖率低至 86%= 5.当样本量很小 (93–97%) 时，S g方法产生了广泛不同的覆盖范围，作为效应量的函数。建议使用小样本量的研究人员使用带有d的 Steiger & Fouladi 方法或带有g的 Hedges & Olkin 方法作为区间估计方法。