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Visualisation 2012 - 2013 Lecture 4. Visualising Comparisons. Brian Mac Namee Dublin institute of Technology Applied Intelligence Research Centre. Origins. This course is based heavily on a course developed by Colman McMahon ( www.colmanmcmahon.com )

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visualisation 2012 2013 lecture 4

Visualisation2012 - 2013Lecture 4

VisualisingComparisons

Brian Mac Namee

Dublin institute of Technology

Applied Intelligence Research Centre

origins
Origins
  • This course is based heavily on a course developed by Colman McMahon (www.colmanmcmahon.com)
  • Material from multiple other online and published sources is also used and when this is the case full citations will be given
visualization of the week
Visualization of the Week

www.pinterest.com/brianmacnamee/great-visualisation-examples/

un visualization of the week
(Un)Visualization of the Week

www.pinterest.com/brianmacnamee/terrible-visualisation-examples/

agenda
Agenda
  • This week we are going to look at means through which we can visualise comparisons between variable values
    • Single variable exploration
    • Simple comparisons
    • Multi distribution comparisons
histogram
Histogram

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

histogram1
Histogram
  • A histogram gives us an in-depth view of a single numeric variable
  • To construct a histogram:
    • Divide the data range into bins
    • Count the occurrence frequency of each bin within the data
    • Normalize the frequency counts
    • Plot a bar graph to show the normalised count for each bin

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

histogram2
Histogram

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

density plot
Density Plot

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

density plot1
Density Plot
  • Note that constructing a density plot requires that the probability density function underlying the data in the histogram is constructed – this takes a bit of work!
  • Common approaches include:
    • Parzen windows
    • Clustering
    • Mixture models
density plot2
Density Plot

From Wikipedia! http://en.wikipedia.org/wiki/Parzen_window

density plot3
Density Plot

From Wikipedia! http://en.wikipedia.org/wiki/Parzen_window

density plot4
Density Plot

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

histogram density plot combined
Histogram & Density Plot Combined

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

histogram3
Histogram
  • The histogram is quite possibly your most important visual data exploration tool!!!
box plot
Box Plot

50

40

30

20

10

0

box plot1
Box Plot

OUTLIERS

Values that fall outside quartile ± 1.5*IQR

VARIABLE VALUES

Values displayed for a single variable

50

MAX

Max value below 3rd Q + 1.5*IQR

40

3rd QUARTILE

The value for the 3rd quartile of the variable values

30

MEDIAN

The median value for the variable

20

1st QUARTILE

The value for the 1st quartile of the variable values

MIN

Min value above 1st Q - 1.5*IQR

10

0

box plot2
Box Plot
  • The components of a box plot are:
    • A thick dark line at the minimum
    • A horizontal lines at the 1st quartiles
    • A horizontal lines at the 3rd quartiles
    • A whisker down to the low value
      • Multiply the IQR by 1.5 to calculate the step
      • The low value is the lowest value above the 1st quartile minus the step
    • A whisker up to the high value
      • The high value is the highest value above the 3rd quartile plus the step
    • Any values outside low and high are marked as outliers
box plot3
Box Plot
  • Some important points about a box plot:
    • 50% of the data occurs between the lower and upper edges of the box
    • The lower 50% of the data occurs below the median
    • The upper 50% of the data occurs above the median line in the box.
    • The lower 25% of the data occurs between the bottom edge of the box and the bottom edge of the lower whisker
    • The upper 25% of the data occurs above the top edge of the box and the top edge of the upper whisker
box plots density functions
Box Plots & Density Functions

From Wikipedia! http://en.wikipedia.org/wiki/Probability_density_function

simple bar graph
Simple Bar Graph

A

B

C

D

E

F

Categories

CATEGORY AXIS

A value is displayed for each category

“Visualize This”, N. Yau, Wiley, 2011

http://shop.oreilly.com/product/0636920022060.do

simple bar graph1
Simple Bar Graph

Average Score

Rating

Survey Research & Design in Psychology Course Evaluation http://ucspace.canberra.edu.au/display/7126/Evaluation+2007

simple bar graph2
Simple Bar Graph

Edward Tufte, “The Quantittative Display of Information”, 2009

pie chart
Pie Chart

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

pie charts
Pie Charts

http://www.uh.edu/engines/epi1712.htm

Google Analytics http://analytics.google.com

pie charts1
Pie Charts

http://www.uh.edu/engines/epi1712.htm

Google Analytics http://analytics.google.com

pie charts2
Pie Charts

Google Analytics http://analytics.google.com

pie charts3
Pie Charts

http://www.uh.edu/engines/epi1712.htm

Google Analytics http://analytics.google.com

pie charts4
Pie Charts

http://www.uh.edu/engines/epi1712.htm

Google Analytics http://analytics.google.com

pie chart2
Pie Chart

William Playfair's "Statistical Breviary,” 1801 via The New York Times

http://www.nytimes.com/2012/04/22/magazine/who-made-that-pie-chart.html?_r=0

pie chart3
Pie Chart

Florence Nightingales’ Crimean War Death Charts via:http://www.uh.edu/engines/epi1712.htm

pie charts5
Pie Charts
  • Pie charts are the subject of a lot of negative comment
    • http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=00018S
    • http://www.juiceanalytics.com/writing/the-problem-with-pie-charts/
    • The main reason is that their descriptive power is based on our ability to interpret differences in angle
  • Pie charts are useful when:
    • We have a small number of categories (< 8)
    • The values sum to a meaningful whole
    • The differences are coarse
doughnut chart
Doughnut Chart

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

tree map
Tree Map

“Visualize This”, N. Yau, Wiley, 2011http://shop.oreilly.com/product/0636920022060.do

billion dollar o gram
Billion-Dollar-O-Gram

www.informationisbeautiful.net/2009/the-billion-dollar-gram/

treemaps
Treemaps
  • Treemaps were originally designed to handle hierarchical structures – such as disk drives – but can be used for non-hierarchical data
  • Treemaps rely on a tiling algorithm to figure out how to position the rectangles
    • We will come back to this!

TreeMap page by Ben Schneiderman (TreeMap Pioneer): http://www.cs.umd.edu/hcil/treemap-history/index.shtml

Early paper on TreeMaps: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isNumber=4467&arNumber=175815&isnumber=4467&arnumber=175815

achtung
Achtung!

Average Score

Rating

Survey Research & Design in Psychology Course Evaluation http://ucspace.canberra.edu.au/display/7126/Evaluation+2007

achtung1
Achtung!

Watch out for bar charts that show an average or other aggregate – these can hide a multitude of detail

Average Score

Rating

Survey Research & Design in Psychology Course Evaluation http://ucspace.canberra.edu.au/display/7126/Evaluation+2007

six nation points2
Six Nation Points

Multiple box plots are a great way to show multiple distributions

overlaid histograms
Overlaid Histograms

http://blogs.sas.com/content/graphicallyspeaking/2012/02/06/comparative-densities/

back to back histograms
Back-to-Back Histograms

http://blogs.sas.com/content/graphicallyspeaking/2012/02/06/comparative-densities/

back to back histograms1
Back-to-Back Histograms

http://blogs.sas.com/content/graphicallyspeaking/2012/02/06/comparative-densities/

conclusions
Conclusions
  • We often need to create visualisationsto compare values
  • There are a range of ways to do this
  • Key things to keep in mind are:
    • Are you comparing values or proportions?
    • Are you comparing single values or distributions?
    • Are you comparing across one or many dimensions?
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