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Misleading Graphs
and Statistics
Questions to Ask When Looking
at Data and/or Graphs
 Is the information presented correctly?
 Is the graph trying to influence you?
 Does the scale use a regular interval?
 What impression is the graph giving
  you?
Why is this graph misleading?
                                                This title tells the reader
                                                what to think (that there
                                                are huge increases in
                                                price).

                                      The scale moves from 0 to 80,000 in
                                      the same amount of space as 80,000 to
                                      81,000.



The actual increase in price is 2,000 pounds, which is less than a 3%
increase.
 The graph shows the second bar as being 3 times the size of the first bar,
 which implies a 300% increase in price.
A more accurate graph:
 An unbiased title




A scale with a
regular interval.




      This shows a more accurate picture of the increase.
Why is this graph misleading?
The scale does not have a regular
interval.
Graphs can be misleading in the
news.
 The margin of error is the amount
  (usually in percentage points) that the
  results can be “off by.”
 Be wary of data with large margins of
  error.
From CNN.com
Problems:
 The difference in percentage points between
  Democrats and Republicans (and between
  Democrats and Independents) is 8% (62 –
  54). Since the margin of error is 7%, it is
  likely that there is even less of a difference.
 The graph implies that the Democrats were 8
  times more likely to agree with the decision.
  In truth, they were only slightly more likely to
  agree with the decision.
 The graph does not accurately demonstrate
  that a majority of all groups interviewed
  agreed with the decision.
CNN.com updates the graph:
What does the top of this
graph show?
•About 12 million people are
downloading music legally.
•Just over 9 million people are
downloading music illegally.

  The bottom of the graph
  is misleading. Why?
  •The graph implies that 1% of
  the iPods are filled with legally
  downloaded music.
  •It implies that the other 99%
  are filled with illegally
  downloaded music.

    Why is this wrong?
What could be in those iPods
besides legally downloaded
music?
 Empty space – most people don’t have
  iPods that are filled to capacity.
 Songs that were added from legally
  purchased CDs.
 Games, calendars, other applications.
 Songs that were downloaded illegally.
It is possible that the rest of the iPod contains some illegally
downloaded music, but it is unlikely that 99% of a person’s
iPod is filled with illegal music.
More information:
 The iPod graphic appeared in Wired
  magazine.
 A quote from the article: “What’s filling all that
  excess capacity? Well, despite the efforts of
  the Recording Industry Association of
  America, nearly a billion songs are traded on
  P2P networks every month.”
 This article was trying to imply that all of the
  excess space is filled with illegal downloads,
  which is likely untrue.
 The statistics for the article were provided by
  the music industry.
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Abuses of statistics

  • 2. Questions to Ask When Looking at Data and/or Graphs  Is the information presented correctly?  Is the graph trying to influence you?  Does the scale use a regular interval?  What impression is the graph giving you?
  • 3. Why is this graph misleading? This title tells the reader what to think (that there are huge increases in price). The scale moves from 0 to 80,000 in the same amount of space as 80,000 to 81,000. The actual increase in price is 2,000 pounds, which is less than a 3% increase. The graph shows the second bar as being 3 times the size of the first bar, which implies a 300% increase in price.
  • 4. A more accurate graph: An unbiased title A scale with a regular interval. This shows a more accurate picture of the increase.
  • 5. Why is this graph misleading? The scale does not have a regular interval.
  • 6. Graphs can be misleading in the news.  The margin of error is the amount (usually in percentage points) that the results can be “off by.”  Be wary of data with large margins of error.
  • 8. Problems:  The difference in percentage points between Democrats and Republicans (and between Democrats and Independents) is 8% (62 – 54). Since the margin of error is 7%, it is likely that there is even less of a difference.  The graph implies that the Democrats were 8 times more likely to agree with the decision. In truth, they were only slightly more likely to agree with the decision.  The graph does not accurately demonstrate that a majority of all groups interviewed agreed with the decision.
  • 10. What does the top of this graph show? •About 12 million people are downloading music legally. •Just over 9 million people are downloading music illegally. The bottom of the graph is misleading. Why? •The graph implies that 1% of the iPods are filled with legally downloaded music. •It implies that the other 99% are filled with illegally downloaded music. Why is this wrong?
  • 11. What could be in those iPods besides legally downloaded music?  Empty space – most people don’t have iPods that are filled to capacity.  Songs that were added from legally purchased CDs.  Games, calendars, other applications.  Songs that were downloaded illegally. It is possible that the rest of the iPod contains some illegally downloaded music, but it is unlikely that 99% of a person’s iPod is filled with illegal music.
  • 12. More information:  The iPod graphic appeared in Wired magazine.  A quote from the article: “What’s filling all that excess capacity? Well, despite the efforts of the Recording Industry Association of America, nearly a billion songs are traded on P2P networks every month.”  This article was trying to imply that all of the excess space is filled with illegal downloads, which is likely untrue.  The statistics for the article were provided by the music industry.