Friday, June 17, 2011

Scatter plots for large samples

While huge datasets have become ubiquitos in fields such as genomics, large datasets are now also becoming to infiltrate research in the social sciences. Data from eCommerce sites, online dating sites, etc. are now collected as part of research in information systems, marketing and related fields. We can now find social science research papers with hundreds of thousands of observations and more.

A common type of research question in such studies is about the relationship between two variables. For example, how does the final price of an online auction relate to the seller's feedback rating? A classic exploratory tool for examining such questions (before delving into formal data analysis) is the scatter plot. In small sample studies, scatter plots are used for exploring relationships and detecting outliers.

Image from http://prsdstudio.com/ 
With large samples, however, the scatter plot runs into a few problems. With lots of observations, there is likely to be too much overlap between markers on the scatter plot, even to the point of insufficient pixels to display all the points.

Here are some large-sample strategies to make scatter plots useful:

  1. Aggregation: display groups of observations in a certain area on the plot as a single marker. Size or color can denote the number of aggregated observations.
  2. Small-multiples: split the data into multiple scatter plots by breaking down the data into (meaningful) subsets. Breaking down the data by geographical location is one example. Make sure to use the same axis scales on all plots - this will be done automatically if your software allows "trellising".
  3. Sample: draw smaller random samples from the large dataset and plot them in multiple scatter plots (again, keep the axis scales identical on all plots).
  4. Zoom-in: examine particular areas of the scatter plot by zooming in
Finally, with large datasets it is useful to consider charts that are based on aggregation such as histograms and box plots. For more on visualization, see the Visualization chapter in Data Mining for Business Intelligence.
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