Current statistical inference methods for task-fMRI suffer from two fundamental limitations. First, the focus is solely on detection of non-zero signal or signal change, a problem that is exacerbated for large scale studies (e.g. UK Biobank, N=40,000+) where the 'null hypothesis fallacy' causes even trivial effects to be determined as significant. Second, for any sample size, widely used cluster inference methods only indicate regions where a null hypothesis can be rejected, without providing any notion of spatial uncertainty about the activation. In this work, we address these issues by developing spatial Confidence Sets (CSs) on clusters found in thresholded Cohen's d effect size images. We produce an upper and lower CS to make confidence statements about brain regions where Cohen's d effect sizes have exceeded and fallen short of a non-zero threshold, respectively. The CSs convey information about the magnitude and reliability of effect sizes that is usually given separately in a t-statistic and effect estimate map. We expand the theory developed in our previous work on CSs for %BOLD change effect maps (Bowring et al., 2019) using recent results from the bootstrapping literature. By assessing the empirical coverage with 2D and 3D Monte Carlo simulations resembling fMRI data, we find our method is accurate in sample sizes as low as N=60. We compute Cohen's d CSs for the Human Connectome Project working memory task-fMRI data, illustrating the brain regions with a reliable Cohen's d response for a given threshold. By comparing the CSs with results obtained from a traditional statistical voxelwise inference, we highlight the improvement in activation localization that can be gained with the Confidence Sets.

中文翻译：

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Cohen 的 d 效应大小图像的置信集

当前任务 fMRI 的统计推断方法存在两个基本限制。首先，重点仅在于检测非零信号或信号变化，在大规模研究（例如 UK Biobank，N=40,000+）中，“零假设谬误”会导致甚至微不足道的影响被确定，这一问题更加严重一样重要。其次，对于任何样本大小，广泛使用的聚类推断方法仅指示可以拒绝零假设的区域，而没有提供有关激活的任何空间不确定性概念。在这项工作中，我们通过在阈值 Cohen 的 d 效应大小图像中发现的簇上开发空间置信集 (CS) 来解决这些问题。我们制作了一个上下 CS 来对 Cohen 所在的大脑区域进行置信度陈述 sd 效应量分别超过和低于非零阈值。CS 传达有关效应大小的大小和可靠性的信息，这些信息通常在 t 统计量和效应估计图中单独给出。我们使用自举文献的最新结果扩展了我们之前关于 %BOLD 变化效果图的 CS 工作中开发的理论（Bowring 等人，2019）。通过使用类似于 fMRI 数据的 2D 和 3D 蒙特卡罗模拟评估经验覆盖率，我们发现我们的方法在低至 N=60 的样本量中是准确的。我们计算了人类连接组计划工作记忆任务 fMRI 数据的 Cohen d CS，说明了在给定阈值下具有可靠 Cohen d 响应的大脑区域。通过将 CS 与从传统统计体素推断获得的结果进行比较，