Categorical exploratory data analysis on goodness-of-fit issues
This work is significant for data scientists and educators, providing a method to better understand the validity and limitations of statistical models when applied to real-world data, particularly regarding goodness-of-fit issues.
The paper addresses the problem of assessing goodness-of-fit in real-world data by proposing Categorical Exploratory Data Analysis (CEDA). It illustrates how CEDA can reveal specific deviations from theoretical distributions, such as the Normal distribution, even when initial visual inspection suggests a good fit.
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.