MISLEADING STATISTICS

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MISLEADING STATISTICS

• Twisting information to your advantage

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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.

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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 authors 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.

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

• In the following presentation, we will show
  you two such misleading graphs, point out their
  errors, and attempt to recreate the same graph
  using more accurate forms of presentation. You
  will see how the same set of information can
  produce two completely different graphs, and
  learn about the many ways in which statistics can
  deceive you.

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This graph is misleading in many ways. Here are
some examples of the most commonly used
graph-manipulation tactics.
First of all, there is the title to consider.
While retail sales do go down in April 2002, the
title doesnt accurately reflect what the rest of
the graph shows. Yes, the sales do rise and fall
over a period of a year and a half, but in
general, they have been steadily rising since
November 1998.
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This graph is misleading in many ways. Here are
some examples of the most commonly used
graph-manipulation tactics.
Second, notice that the y-axis does not begin at
zero, but at 225 billion. This has the
unfortunate effect of making the rising slope
shown in the graph much steeper than it actually
is.
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This graph is misleading in many ways. Here are
some examples of the most commonly used
graph-manipulation tactics.
Third, the little white box that shows the rate
of change from pervious months only includes the
last three months in the graph. This immediately
biases the graph in favor of the title, as it
shows that sales have actually gone down since
February. A reader just looking at the box will
not know that sales have also gone down in May
and September 1999, and that these did not affect
the rising number sales one bit.
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This graph is misleading in many ways. Here are
some examples of the most commonly used
graph-manipulation tactics.
Fourth, note that the year 1999 is written under
June and July, and not January. This may be a
minor transgression, but it will certainly lead
some readers to believe that the time period
spans three whole, consecutive years and not
fragments of a year.
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This graph is misleading in many ways. Here are
some examples of the most commonly used
graph-manipulation tactics.
One final observation Is it fair to compare
retail sales of the months of a year all
together? Christmas in December, for example,
would prompt gift buying, but slower months like
February might now have any at all. Wouldnt it
be much fairer to compare the same months and
calculate how much it has grown over the year?
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On this second graph, the y-axis begins on
zero, therefore making the rising slope much less
dramatic. When presented like this it is also
harder to tell which bars are higher and lower.
The last two bars, for example March and April
look almost exactly the same on this graph. If
the reader wasnt told that the sales had
actually gone down from March in April, he would
never know. The title, likewise, has been changed
to something that can encompass all aspects of
this graph. In addition, instead of labeling a
group of months with one year, we have given each
month its own year so that its easier to read.
However, this graph still does not address the
problem of comparing all months together as
equals. In our next graph, we will show you what
that might look like.
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Comparing the months of consecutive years
yields yet another perspective to the picture.
From this graph, it is easy to see that sales
have steadily risen for each month, and by a
fairly predictable percentage at that. Nearly all
the months are rising by the same margin from one
year to the next. Even April sales, which the
original graph proclaimed was falling, have risen
compared to its sales from the previous year.
Once again, while the original graph seems to
be trying to convince us that April sales have
very obviously fallen, these two graphs tell us
the opposite. Appropriately, the title for this
third graph has been changed completely to give
the opposite minute.
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Of course, there are many different ways to lie
with statistics, and now well show you how it
can be done with a pictograph.
Of course, there are many different ways to lie
with statistics, and now well show you how it
can be done with a pictograph. The most
deceptive aspect of this graph is the way in
which it was drawn. Firstly, the perspective
puts barrel 1979 at the forefront and barrel 1973
at the back. This effectively draws readers
eyes to the 1979 barrel first and then forces him
read the rest of the years in descending order.
Supporting this deceptive tactic is the fact that
only the foremost barrels have complete year to
read. The rest are indicated with only the last
two digits, as in 76. Obviously, the makers of
the graph intend for the audience to read in
reverse chronological order, which has the effect
of making oil prices seem to fall.
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Of course, there are many different ways to lie
with statistics, and now well show you how it
can be done with a pictograph.
Secondly, the perspective makes it hard to judge
the numerical difference between each barrel.
For example, even though barrel 1975 appears to
be over two thirds the height of 1976, in
reality, the difference between them is only
0.95. Likewise, barrel 1973 seems less than
half the height of 1974, yet they differ by a
whopping 8.54! the effect of making oil prices
seem to fall.
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Of course, there are many different ways to lie
with statistics, and now well show you how it
can be done with a pictograph.
A third misleading aspect is that this pictograph
doesnt contain a scale or axis of any kind.
Without it, the readers attention might be
directed to the area of each barrel instead.
Numerically, the smallest barrel should only be
about one 1/5 of the largest barrel, but in terms
of area, the ratio is about 1/25. This makes the
different between the two much larger than it
actually is.
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Of course, there are many different ways to lie
with statistics, and now well show you how it
can be done with a pictograph.
Lastly, the way in which the barrels are labeled
seem somewhat awkward. Shouldnt the prices be
on the barrel instead of years? Prices written
on the barrel will clarify that it is the cost
that is changing, not the years. And with more
space to indicate years, readers wont be forced
to read in reverse.
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This graph neatly depicts the steadily rising
prices of crude oil, and shows sudden rises or
drops. Each bar represents a number by its
height without using fancy images to distract the
reader. The presence of the x and y-axis also
make it much more organized. While the original
graph tended to overstate small differences and
gloss over wide gaps, this graph is much more
honest. One can see that the largest rise occurs
between 1973 and 1973, and that it continues to
rise by smaller amounts steadily over the next
five years. The years on the x-axis are all
clearly marked in chronological order as well so
that it is easy for readers to understand.
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For this type of information, using a line
graph may be even more useful than a bar graph.
With a line to define the rise of fall of oil
prices, it is all the more obvious what the shape
of the changing rates look like. This graph even
seems to accentuate the huge rise between 1973
and 1974. The biggest benefits of a using a line
graph, however, lies in the fact that each point
is marked with small, accurate dots. These are
much easier to read than bars, and the line
between them outlines the contour of the rise.
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What makes statistical information reliable and
accurate?
To make sure statistics are accurate and
reliable, one must keep a number of things in
mind. Here are the some of the most important
points to remember The first and most
important is the collection of information. Its
alarmingly easy to make graphs with missing
figures, and this only produces inaccurate
results. Before making any graph, it is wise to
make that the data is sufficient. This is
especially true in surveys, where the accuracy of
the results is in direct proportion to the number
of people surveyed. Next to quantity in
importance is quality. There is little point in
making a graph with inaccurate information.
Even with accurate information, however, you must
know which is the best way of using and
presenting it. Many perfectly accurate
statistics become misleading when they are
unfairly compared. You would not, for example,
compare the average grades of a small school to
the average grades of a large school without
making allowances for the larger diversity of
students. Therefore, when presenting data, care
must be taken to prevent this.
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What makes statistical information reliable and
accurate?
To make sure statistics are accurate and
reliable, one must keep a number of things in
mind. Here are the some of the most important
points to remember The first and most
important is the collection of information. Its
alarmingly easy to make graphs with missing
figures, and this only produces inaccurate
results. Before making any graph, it is wise to
make that the data is sufficient. This is
especially true in surveys, where the accuracy of
the results is in direct proportion to the number
of people surveyed. Next to quantity in
importance is quality. There is little point in
making a graph with inaccurate information.
Even with accurate information, however, you must
know which is the best way of using and
presenting it. Many perfectly accurate
statistics become misleading when they are
unfairly compared. You would not, for example,
compare the average grades of a small school to
the average grades of a large school without
making allowances for the larger diversity of
students. Therefore, when presenting data, care
must be taken to prevent this.
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What makes statistical information reliable and
accurate?
Although this graph is pleasing to look at, it
can also be confusing. The author meant for the
Number of Buyers to be calculated by the height
of each picture, but the readers attention will
be more focused on area. What makes it even more
biased is that each monitor on the graph is a
Macintosh.