The central limit theorem (CLT) is one of the most important theorems in statistics, and it is often introduced to social sciences researchers in an introductory statistics course. However, the recent replication crisis in the social sciences prompts us to investigate just how common certain misconceptions of statistical concepts are. The main purposes of this article are to investigate the misconceptions of the CLT among social sciences researchers and to address these misconceptions by clarifying the definition and properties of the CLT in a manner that is approachable to social science researchers. As part of our article, we conducted a survey to examine the misconceptions of the CLT among graduate students and researchers in the social sciences. We found that the most common misconception of the CLT is that researchers think the CLT is about the convergence of sample data to the normal distribution. We also found that most researchers did not realize that the CLT applies to both sample means and sample sums, and that the CLT has implications for many common statistical concepts and techniques. Our article addresses these misconceptions of the CLT by explaining the preliminaries needed to understand the CLT, introducing the formal definition of the CLT, and elaborating on the implications of the CLT. We hope that through this article, researchers can obtain a more accurate and nuanced understanding of how the CLT operates as well as its role in a variety of statistical concepts and techniques.

中文翻译：

---

如何清晰地思考中心极限定理。


中心极限定理（CLT）是统计学中最重要的定理之一，经常在统计学入门课程中向社会科学研究人员介绍。然而，最近社会科学领域的复制危机促使我们调查统计概念的某些误解有多普遍。本文的主要目的是调查社会科学研究人员对 CLT 的误解，并通过以社会科学研究人员易于理解的方式澄清 CLT 的定义和属性来消除这些误解。作为我们文章的一部分，我们进行了一项调查，以调查研究生和社会科学研究人员对 CLT 的误解。我们发现，对 CLT 最常见的误解是，研究人员认为 CLT 是关于样本数据向正态分布的收敛。我们还发现，大多数研究人员没有意识到 CLT 适用于样本均值和样本总和，并且 CLT 对许多常见的统计概念和技术有影响。我们的文章通过解释理解 CLT 所需的准备工作、介绍 CLT 的正式定义并详细阐述 CLT 的含义，解决了对 CLT 的这些误解。我们希望通过本文，研究人员能够更准确、更细致地了解 CLT 的运作方式及其在各种统计概念和技术中的作用。