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

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

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

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book that identifies misrepresentations (graphic and numeric) is How to Lie with Statistics by Huff The examples are out of date (the book was first published in 1954) … but the invalid techniques are still used today

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

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

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

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

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

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

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

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

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

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

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

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