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If the aphorism "All models are wrong"- George Box, continues to be true indata analysis, particularly when analyzing real-world data, then we shouldannotate this wisdom with visible and explainable data-driven patterns. Suchannotations can critically shed invaluable light on validity as well aslimitations of statistical modeling as a data analysis approach. In an effortto avoid holding our real data to potentially unattainable or even unrealistictheoretical structures, we propose to utilize the data analysis paradigm calledCategorical Exploratory Data Analysis (CEDA). We illustrate the merits of thisproposal 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 ratherwell by first glance. We apply CEDA to bring out where and how each data fitsor deviates from the model shape via several important distributional aspects.We also demonstrate that CEDA affords a version of tree-based p-value, andcompare it with p-values based on traditional statistical approaches. Along ourdata analysis, we invest computational efforts in making graphic display toilluminate the advantages of using CEDA as one primary way of data analysis inData Science education.

Categorical exploratory data analysis on goodness-of-fit issues