06 Data Visualization

Visualization¶

Display of data in a graphical/tabular format

Helps us understand the data

Why is visualization important?¶

Widely different distributions can have the same statistical properties

Below is the Anscombe’s quartet

Note¶

Use the correct minimum & max range, such that only possible values are included

• Do not skew the axis
• For eg: for human body temperature, you should show 98-105 F; you shouldn’t start at 0

Uni-Variate¶

Box/Box-Whiskers Plot¶

Helps understand the range and central tendancy of a variable

1D Histogram¶

Visualizes the frequency distribution of attribute

Relative uncertainty of each bin frequency \(\propto \dfrac{1}{\sqrt{\text{count}}}\) 

Categorical Data¶

Each category will have a line denoting the frequency associated with that category

Continuous Data¶

• Apply binning
  • Usually equal-width binning
• Each bin will be treated as a different category
• Now each bin will have a line denoting the frequency associated with that category

The convention of analyzing these bins

• Values are left-inclusive and right-exclusive
• Last bin is right-inclusive

~ Oracle Docs

Limitations¶

• Shape may change dramatically depending on bin settings
• Bins with few counts have high statistical uncertainty
• Interpretation can be difficult without huge amounts of data

Q-Q Plot¶

Quantile-Quantile plot comparing a distribution’s quantiles with quantiles of a known distribution (such as Normal distribution)

Bi-Variate¶

Scatter Plot¶

Line Plot¶

2D Histogram¶

Helps understand frequency of co-occurance of 2 attributes

Pair Plot¶

Basically a matrix of scatter plots

Stem & Leaf Plots¶

Understand the distribution of values of an attribute

Useful when there aren’t many values

Steps¶

• Split values into groups, where each group contains those values that are the same except for the last digit
• Each group becomes a stem, while the last digit of a group are the leaves
  • Stems will be the higher-order digits
  • Leaves will be the lower-order digits
• Plot stems vertically and leaves horizontally

Tri-Variate¶

Contour Plots¶

Used for spacial data

Multi-Variate¶

Parallel Coordinates¶

Conditional Quantitative Plots¶

• Bin quantitative data
• Make different plots

This will be useful for error distribution inspection

Cheat Sheet¶

Data Visualization Guidelines¶

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