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Topic: Research on "Twice as big"
Replies: 19   Last Post: Feb 27, 2011 1:15 PM

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Jonathan Groves

Posts: 2,068
From: Kaplan University, Argosy University, Florida Institute of Technology
Registered: 8/18/05
Re: Research on "Twice as big"
Posted: Jan 23, 2011 11:27 PM
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On 1/23/2011 at 2:22 am, I had written (in part):

> A lot of graphs will use this error--perhaps
> intentionally--to distort
> proportions. For instance, one graph I had seen in a
> math book that
> discusses various ways that graphs are distorted had
> drawn a graph of
> the spending value of the dollar at the time the book
> was written (which
> was within the last few years) in terms of the dollar
> from about 1980
> or so. Today's dollar is equivalent to about 43 or
> so cents back
> then, which is roughly half. The graph draws dollar
> bills in a way that
> the dollar bill for today had length and width about
> half of the length
> and width of the dollar bill representing a dollar
> from the previous
> generation. That is, the graph visually suggests
> that today's dollar
> has about only a quarter of the spending value of
> last generation's dollar
> rather than half. I will have to track down that
> book of mine if I am
> to get the title and author. My first guess a few
> minutes ago was
> incorrect. So were my next several guesses.
> I don't know if it is the same book or not, but I
> remember another
> example involving either prices or uses of oil over
> time, and the
> graph drew oil drums in such a way so that twice the
> amount being
> measured was represented by an oil drum 8 times as
> large.
> Such examples might not answer your original
> question, but they
> do illustrate this same error involving areas and
> volumes.


I had tracked down that book this evening. It is Robert Blitzer's
third edition of "Introductory and Intermediate Algebra for College

The graph involving the spending amounts of the dollar compares
the worth of a dollar in 1990, 1995, 2000, and 2005 in terms of 1980's
dollar. The 1990 dollar is 63 cents in terms of the 1980 dollar.
The 1995 dollar is 54 cents. The 2000 dollar is 48 cents. And
the 2005 dollar is 43 cents.

Here is Blitzer's explanation of the graph:

"Although the length of each dollar bill is proportional to its
spending power, the visual display varies both the length and
width of the bills to show the diminishing power of the dollar over
time. Because our eyes focus on the areas of the dollar-shaped
bars, this creates the impression that the purchasing power of
the dollar diminished even more than it really did. If the area
of the dollar were drawn to reflect its purchasing power, the 2005
dollar would be approximately twice as large as the one shown in
the graphic display" (p. 163, Section 2.6).

He has a similar display for oil barrel prices over time from 1999
to 2005. Both the radius and height of the barrels are proportional
to their prices, which gives the impression that a price in one
year being about half the price of another year appears to be
about 1/8 instead of 1/2. So the graph suggests that oil prices
have flucuated much more than they actually did.

Jonathan Groves

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