关于拟合优度问题的分类探索性数据分析
Categorical exploratory data analysis on goodness-of-fit issues
摘要：
如果“所有模型都是错误的”这句格言在数据分析中仍然适用，特别是在分析真实世界的数据时，那么我们应该用可见的和可解释的数据驱动模式来诠释这一智慧。这种注释可以批判性地揭示统计建模作为数据分析方法的有效性和局限性。为了避免将我们的真实数据保持在可能无法实现甚至不切实际的理论结构中，我们建议利用称为分类探索性数据分析（CEDA）的数据分析范式。我们从拟合优度的角度说明了这一建议的优点与两个现实世界的数据集。在这两个数据集中，乍一看，正态分布的钟形似乎非常适合。我们应用CEDA，通过几个重要的分布方面，找出每个数据在哪里以及如何拟合或偏离模型形状。我们还证明了CEDA提供了一个版本的基于树的p值，并将其与基于传统统计方法的p值进行比较。在我们的数据分析中，我们将计算工作投入到图形显示中，以阐明使用CEDA作为数据科学教育中数据分析的主要方式之一的优势。
英文摘要：
If the aphorism "All models are wrong"- George Box, continues to be true in data analysis, particularly when analyzing real-world data, then we should annotate this wisdom with visible and explainable data-driven patterns. Such annotations can critically shed invaluable light on validity as well as limitations of statistical modeling as a data analysis approach. In an effort to avoid holding our real data to potentially unattainable or even unrealistic theoretical structures, we propose to utilize the data analysis paradigm called Categorical Exploratory Data Analysis (CEDA). We illustrate the merits of this proposal with two real-world data sets from the perspective of goodness-of-fit. In both data sets, the Normal distribution's bell shape seemingly fits rather well by first glance. We apply CEDA to bring out where and how each data fits or deviates from the model shape via several important distributional aspects. We also demonstrate that CEDA affords a version of tree-based p-value, and compare it with p-values based on traditional statistical approaches. Along our data analysis, we invest computational efforts in making graphic display to illuminate the advantages of using CEDA as one primary way of data analysis in Data Science education.
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