1. Graphical Misrepresentations of Data
Chapter 2 Section 3
Graphical Misrepresentations
of Data

2. Chapter 2 – Section 3 Learning objectives
Describe what can make a graph misleading or deceptive 1

3. Chapter 2 – Section 3 “Lies, damn lies, and statistics”
“Figures lie and liars figure”
Statistics displays can distort the truth
Unintentional distorting … mislead
Intentional distorting … deceive
There are several common errors, such as
Charts where the visuals and the numbers do not correspond
Charts that have an artificial base point to exaggerate the differences
“Lies, damn lies, and statistics”
“Figures lie and liars figure”
“Lies, damn lies, and statistics”
“Figures lie and liars figure”
Statistics displays can distort the truth
Unintentional distorting … mislead
Intentional distorting … deceive

4. Chapter 2 – Section 3
The classic short book that identifies misrepresentations (graphic and numeric) is How to Lie with Statistics by Huff
The examples are out of date (the book was first published in 1954) … but the invalid techniques are still used today

5. Chapter 2 – Section 3 Common errors are Inaccurate displays
Unclear vertical scale
Truncated vertical scale
Misleading dimensions

6. Chapter 2 – Section 3
Despite advances in publishing and statistical software, there are still simple numeric mistakes
Lengths of bars in bar charts and histograms that do not match their frequencies
Slices of pie charts that are not proportional to their relative frequencies

7. Chapter 2 – Section 3 This pie graph is deliberately incorrect
The red region is too small
The aqua region is too large
Pie charts are sometimes incorrect in this way

8. Chapter 2 – Section 3
Some charts have a vertical scale that is unclear
The scale is possibly not labeled
The zero point of the scale is unclear
In these graphs, the order of the sizes is accurate, but the relative comparisons can be misleading

9. Chapter 2 – Section 3 In this graph, it is unclear
Where the vertical scale begins (bottom of or top of the shirts) starts
What the scale increments are

10. Chapter 2 – Section 3
The vertical scale is truncated when the vertical scale does not start at 0
When the vertical scale starts at a higher number, the differences between the bars is exaggerated
For some data, magnifying the differences is important
For some data, magnifying the differences is misleading
The vertical scale is truncated when the vertical scale does not start at 0

11. Chapter 2 – Section 3
The two graphs show the same data … the difference seems larger for the graph on the left
The vertical scale is truncated on the left

12. Chapter 2 – Section 3
When there is interest in small changes – showing day to day stock prices for example – then the graph on the left is appropriate

13. Chapter 2 – Section 3
When there is interest in the totals – showing yearly salaries for example – then the graph on the right is appropriate

14. Chapter 2 – Section 3
Some charts are made visually more attractive by using symbols and graphics instead of plain bars and lines
If one category has twice the frequency of another, that graphic is doubled in size
If the graphic is a three dimensional graphic, then doubling each dimension increases the volume by eight times which is misleading
Some charts are made visually more attractive by using symbols and graphics instead of plain bars and lines
Some charts are made visually more attractive by using symbols and graphics instead of plain bars and lines
If one category has twice the frequency of another, that graphic is doubled in size

15. Chapter 2 – Section 3
The gazebo on the right is twice as large in each dimension as the one on the left
However, it is much more than twice as large as the one on the left
Original
“Twice” as large

16. Summary: Chapter 2 – Section 3
Displays are powerful for representing data
Displays are also powerful for misrepresenting data
Avoiding distortions in your own work is very important
Recognizing distortions in other people’s work is very important also