  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.
