12.3 Violin plots and bean plots

Violin and bean plots offer a more detailed view of data distribution than traditional box plots. They combine aspects of box plots and density plots, showing the probability density at different values and allowing for better understanding of modality and skewness.

These plots are powerful tools for visualizing complex data distributions. While they may be less familiar to general audiences, they provide valuable insights into data characteristics that might be missed with simpler visualization methods.

Violin Plots and Bean Plots

Understanding Violin and Bean Plots

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• Visualize the distribution of a dataset by combining aspects of box plots and density plots
• Display the probability density of the data at different values
  • Width of the "violin" is proportional to the density (wider sections represent higher density, narrower sections represent lower density)
• Created by estimating the kernel density of the data and mirroring the density curve to create the symmetric violin shape

Bean Plots: Adding Granularity to Violin Plots

• Similar to violin plots but add a rug plot of individual data points to the density shape
• Display the actual data points as small lines (the "beans") scattered within the mirrored density shape
  • Allows for a more detailed view of the data distribution
• Can be split to show multiple distributions side-by-side for comparison (different categories or groups within the data)
• Median and interquartile range are sometimes included within the density shape, similar to a box plot, to provide additional summary statistics

Violin Plots vs Box Plots

Advantages of Violin and Bean Plots

• Provide a more detailed representation of the data distribution compared to box plots
  • Box plots only show summary statistics (median, quartiles, and outliers)
• Density shape allows for a better understanding of the modality, skewness, and potential outliers in the data
  • Box plots do not show the underlying distribution, which can be misleading for multimodal or non-standard shaped data
• Bean plots have the added advantage of displaying individual data points
  • Helps identify clusters, gaps, or outliers that may not be apparent in the density shape alone

Disadvantages of Violin and Bean Plots

• Can become less readable when comparing many distributions side-by-side
  • Density shapes may overlap or become cluttered
  • Box plots are more compact and easier to interpret when comparing a large number of distributions
• May be less familiar to a general audience compared to box plots, which are more widely used and understood

Creating Violin and Bean Plots

Using Statistical Software Packages

• Most statistical software packages have built-in functions for creating violin and bean plots
  • R:

    vioplot()

    function from the 'vioplot' package for violin plots,

    beanplot()

    function from the 'beanplot' package for bean plots
    • Basic syntax for a violin plot:

      vioplot(x, ...)

    • Basic syntax for a bean plot:

      beanplot(x, ...)

  • Python: Seaborn library provides

    violinplot()

    function for violin plots and

    swarmplot()

    function for plots similar to bean plots
    • Basic syntax for a violin plot:

      sns.violinplot(x=, y=, data=, ...)

    • Basic syntax for a swarm plot:

      sns.swarmplot(x=, y=, data=, ...)

Considerations When Creating Plots

• Choice of kernel density estimation parameters, such as bandwidth, can affect the smoothness of the density shape
• Bandwidth selection is important to ensure an accurate representation of the underlying distribution
  • Too small a bandwidth may result in an overly noisy density estimate
  • Too large a bandwidth may result in an overly smoothed density estimate, obscuring important features

Distribution Density and Shape

Interpreting the Shape of Violin and Bean Plots

• Shape provides insights into the characteristics of the data distribution
  • Modality: Unimodal distributions have a single peak, bimodal or multimodal distributions have multiple peaks (indicating distinct clusters or subgroups)
  • Skewness: Asymmetric density shape with a longer tail on one side (right-skewed: longer tail on the right, left-skewed: longer tail on the left)
  • Spread: Width of the density shape at different points represents the density of data at those values (wider sections: higher concentration, narrower sections: lower concentration)
• Unusual or unexpected shapes (long tails or isolated clusters) can indicate outliers or subgroups that may require further investigation

Comparing Multiple Distributions

• Differences in density shapes can highlight disparities in the central tendency, spread, or modality across categories or groups
• Side-by-side comparison of violin or bean plots allows for easy identification of differences in distribution characteristics
  • Shifts in the median or interquartile range
  • Changes in the shape, skewness, or modality of the distributions
  • Presence of outliers or distinct subgroups within specific categories