Mastering Distribution Plots for Explanatory Data Analysis

Understanding the shape and properties of data distributions is a fundamental early step in the data science workflow. This guide will comprehensively cover leveraging distribution plots to visually assess and present key aspects of a dataset‘s distribution.

We will focus on pragmatic techniques for constructing, customizing, and applying interactive distribution plots powered by the Plotly Python graphing library.

Overall, you will gain expert-level skills in:

• Statistical foundations behind histograms, kernel density estimation, and choice of bandwidth
• Constructing complex statistical chart layouts with Plotly‘s figure_factory module
• Customizing axis scales, colors, and style options for presentation-ready plots
• Leveraging distribution plots for rapid exploratory data analysis
• Combining distribution visualization with statistical hypothesis testing

Following this guide will provide a very solid grasp of distribution plots for both analysis and communication of data properties.

Statistical Background

First, let‘s ground the foundations in the statistical techniques behind the central chart types used:

Histograms

A histogram divides continuous data into binned intervals and counts observations that fall in each bin. This aggregates to produce a visual representation of the data distribution. Key aspects are:

• Bin size impacts smoothing level
• Visualizes central tendency, variability, outliers
• Approximates underlying distribution

Kernel density estimation

A kernel density estimate applies kernel functions (e.g. Gaussian) to smooth a discrete distribution into a continuous density curve. Choice of kernel and bandwidth are key considerations:

• Wider bandwidth = more smoothing
• Data-driven automated bandwidth selections available
• Visualizes distribution shape

Together, histograms and KDE plots complement each other to provide aggregate distribution analysis and visualization for trend analysis, outlier detection, feature engineering, and more.

Constructing Distribution Plots

Python‘s Plotly library provides a very convenient figure_factory module for building complex statistical charts with minimal code.

The create_distplot() function consolidates generating histograms, KDE plots, rug plots and more into one step:

import plotly.figure_factory as ff

fig = ff.create_distplot(hist_data=[‘data‘])

Passing in time-series data arrays automatically handles binning, density estimation, assigning colors, and additional chart elements.

Let‘s walk through an example with 100 random normal data points:

import numpy as np 
data = np.random.randn(100)

import plotly.figure_factory as ff
fig = ff.create_distplot([data])
fig.show()

This outputs an interactive distribution plot:

Customizing the histogram bin size, kernel density bandwidth, colors etc can all be configured through additional parameters.

Next, we will demonstrate more advanced applications.

Interactive Visual Analysis with Customization

Beyond basics, figure_factory allows crafting customized publication-quality charts adapted to reveal unique aspects of your data.

Let‘s look at average housing prices over time in San Francisco:

import pandas as pd

sf_housing = pd.read_csv(‘./sf_housing.csv‘, index_col=‘Year‘)
fig = ff.create_distplot(sf_housing)

This reveals a clear exponential trend in prices over recent decades. However, the exponential y-axis scale compresses recent data.

We can switch to a log scale and also color code the series by decade:

fig.update_layout(
    yaxis=dict(
        type=‘log‘,
        title=‘Prices by Decade‘
    )
)

fig.update_traces(marker_color=[‘red‘, ‘green‘, ‘blue‘])

This improved visualization exposes the extreme growth in prices, now clearly differentiated by decade. The log scale draws out the distribution shape rather than compressing recent data.

Many more custom styling and configuration options are available through Plotly–this example just touches the surface.

Now that we‘ve covered the fundamentals of constructing and customizing distribution plots, we‘ll discuss how to apply these techniques to accelerate exploratory data analysis.

Applications in Exploratory Data Analysis

Combining histograms, kernel density estimates, and related chart elements into distribution plots uniquely equips these charts for rapid exploratory analysis.

By condensing multiple aspects of distribution analysis into one chart, we can conveniently evaluate properties like:

• Unimodality vs multimodality
• Presence of outliers
• Skewness
• Clustering tendencies

Let‘s demonstrate an example workflow for assessing and comparing predictor variables in a regression task:

We‘ll use the Ames housing dataset containing different measurements of properties sold in Ames, Iowa.

First we load the data and variables of interest:

import pandas as pd

data = pd.read_csv(‘./ames.csv‘)
y = data[‘SalePrice‘]
X = data[[‘LotArea‘, ‘1stFlrSF‘,‘TotRmsAbvGrd‘]]

Our target is sale price, while we have three predictor variables for living area, lot area and total rooms.

Using distribution plots, we can visually inspect relationships:

import plotly.figure_factory as ff

for col in X.columns:
   fig = ff.create_distplot([X[col], y])
   fig.show()

• Living area vs price show concentration at low median values, with very long tails likely representing luxury properties
• Lot area distribution is right skewed, concentrations between typical lot sizes
• Total rooms show close relationship with price with similar distribution shapes

This quick analysis reveals potential conditioning is likely needed between total rooms and price to account for their non-linear relationship for modeling. Insights like these would be difficult to extract from statistical descriptions alone.

In this manner, leveraging distribution plots early when exploring data can powerfully accelerate feature engineering and model decisions before formal hypothesis testing.

Finally, let‘s discuss combining distribution plot techniques with statistical tests to quantify insights.

Integrating Statistical Hypothesis Testing

While distribution plots provide visualization power, statistical hypothesis tests add numeric measures of distribution similarities.

The Kolmogorov-Smirnov (K-S) test in SciPy compares two empirical distributions, with the null hypothesis being that the samples are drawn from the same distribution.

We can quantify the relationship visualized above between total rooms and home prices.

First repeating the visualization:

rooms_dist = ff.create_distplot([X[‘TotRmsAbvGrd‘], y])

Then applying K-S test:

from scipy import stats
stats.ks_2samp(X[‘TotRmsAbvGrd‘], y)

        K-S Test Statistic   p-value
     0.03624732492250326   0.10713197882633852

With p > 0.05, we fail to reject null hypothesis – indicating while distributions differ, rooms are likely useful predictor of price.

This demonstrates how statistical tests can augment and quantify the visual insights from distribution plots. Together they form a very effective analysis toolkit.

In summary, we covered leveraging Plotly‘s figure_factory module to:

• Construct histograms, kernel density estimates and distribution plots with Python
• Customize plots for exploratory analysis and explanatory presentation
• Apply distribution visualization throughout the data science workflow
• Couple with statistical hypothesis tests like K-S to quantify distribution relationships

You now have expert skills in harnessing distribution plots for deeper data insight!

For more techniques, see the Plotly Graphing Library documentation at: https://plotly.com/python/.

I welcome any feedback or questions on applying these concepts to your work.