Misleading Graphs and Statistics

When math can be used to lie.

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. – H.G. Wells

Indeed, statistics may be one of our most effective and efficient vehicles for communicating information. It is the natural inclination of people to trust numbers over words, and statistics present numbers in an attractive format that even the most innumerate man can follow. In addition, statistics can be presented in a wide variety of forms, from line graphs to tables to pie charts. Each performs its own unique function and offers information from a new perspective.

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. – H.G. Wells

Yet with every benefit comes a setback. Many people do not realize that numbers in a graph can be easily manipulated to reflect the author’s own wishes. The problem with graphs is that even with missing information, incomplete figures, and vague captions, they can still be presented with reasonable realism. People have grown so accustomed to seeing graphs that they accept its information unquestionably.

Questions to Ask When Looking at Data and/or Graphs Is the title trying to lead you? Does the Y-axis start at zero? Is the graph trying to influence you? Does the scale use a regular interval? Is the graph angled? Are the bars the same width? 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 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.

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

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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