Standard meta-analysis requires the quantity of interest and its estimated variance to be reported for each study. Datasets that lack such variance information pose important challenges to meta-analytic inference. In a study with continuous outcomes, only sample means and sample sizes may be reported in the treatment arm. Classical meta-analytical technique is unable to apply statistical inference to such datasets. In this paper, we propose a statistical tool for testing equal means between two groups in meta-analysis when the variances of the constituent studies are unreported, using pivot inference based on the exact t-distribution and the generalized likelihood ratio. These are considered under a fixed-effect model. In simulations, the type I errors and power probabilities of the proposed tests are investigated as metrics of their performance. The t-test statistic provides type I errors very close to the nominal significance level in all cases and has large power. The generalized likelihood ratio test statistic performs well when the number of studies is moderate-to-large. The performance of our tests surpasses that of the conventional test, which is based on the normal distribution. The difference is especially pronounced when the number of studies is small. The distribution given by our tests is also shown to closely follow the theoretical distribution.

中文翻译：

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当未报告研究特定的差异时，对荟萃分析中均值差异的简单检验

标准的荟萃分析要求为每项研究报告感兴趣的数量及其估计的方差。缺乏此类方差信息的数据集对元分析推理提出了重要挑战。在具有连续结果的研究中，治疗组中只能报告样本均值和样本量。经典的元分析技术无法将统计推断应用于此类数据集。在本文中，我们提出了一种统计工具，用于在未报告组成研究的方差时，使用基于精确 t 分布和广义似然比的枢轴推断来测试荟萃分析中两组之间的相等均值。这些是在固定效应模型下考虑的。在模拟中，所提出的测试的 I 类错误和功率概率被研究为它们的性能指标。t 检验统计量提供的 I 类误差在所有情况下都非常接近名义显着性水平，并且具有很大的功效。当研究数量为中到大时，广义似然比检验统计量表现良好。我们的测试的性能超过了基于正态分布的传统测试。当研究数量很少时，差异尤其明显。我们的测试给出的分布也显示出与理论分布密切相关。这是基于正态分布的。当研究数量很少时，差异尤其明显。我们的测试给出的分布也显示出与理论分布密切相关。这是基于正态分布的。当研究数量很少时，差异尤其明显。我们的测试给出的分布也显示出与理论分布密切相关。