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of more than $1,083 of their own money, most people did not realize that the “average”
included some very wealthy people who would gain to a much greater extent from the
cuts. The figure for the middle 20 per cent of income distribution was calculated by
the Urban-Brookings Tax Policy Center to be only $227 in 2003.62
Talk about “average income” of a community can be very unclear. Are children
and retired people included in the mean figure or only salaried people? Are all sources
of revenue taken into account? What about court settlements? When there is talk
of “family income,” the meaning becomes obscured by lack of precision as to what
constitutes a “family.”
2. The Semi-Attached Figure. To understand the state of a country or corporation, it
is important to know on what various figures are based. If more people are killed in
plane crashes than, say, 50 years ago, it does not follow that flying is less safe, because
the number of planes flying—and having accidents—has increased. The relevant base
is the number of fatalities per passenger mile.
When there is a lot of talk about increased employment, caution is needed before
assuming that the population as a whole is doing better. Are casual, part-time, and
non-benefit-paying jobs included in the employment statistics? Is there a greater pro-
portion of these “McJobs” than earlier? We need to answer these questions first in
order to learn whether things are better than before. Also, it would be easy for govern-
ments to simply recategorize a percentage of the population who have been out of a
job for a stipulated length of time as no longer being in the labour force. If they are
not in the labour force, they are not counted as unemployed, but they still do not have
a job. Care is needed to verify that no such manipulation of the base for computing
unemployment has taken place.
In Canada much work is seasonal, and so a better indication of whether employ-
ment opportunities are better or worse over time is to present the “seasonally adjusted”
figure of those employed. Likewise, when salary figures over a period of years are com-
pared, the relevant figure is more likely to be the salaries in constant dollars, which
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is to say, dollars adjusted for inflation. When government spending on health is concerned, the relevant figure may not only be that of constant dollars but also the
amount of money spent on an age-factored population, since it is well-known that
health costs increase for an elderly population. For education expenses, a relevant
figure, in addition to the global budget, is the amount provided per student.
When it comes to university enrolment figures, those universities with a large
number of part-time students will be misrepresented if comparisons are made count-
ing only full-time students. The same university may have a hard time keeping track
of enrolment growth over time. One way of including the part-time component is to
count ful -time course equivalents, so that four or five courses taken by different part-
time students in a given year would equal one ful -time course equivalent.
In considering a statistical base, one must ask: will this base provide the right kind
of figures to reflect adequately, for purposes at hand, the situation in the country, cor-
poration, institution, etc.? Of course, there are many interests that create pressures to
give something less than an adequate picture. In labour negotiations, it helps manage-
ment to present a financial picture of the company that makes finances appear precari-
ous. When presenting a report to investors, it helps to raise capital if a rosy picture is
presented. Different accounting procedures (for example, whether estimated capital
expenses are amortized slowly or rapidly, conservatively or optimistically) can alter the
picture presented to respective audiences.
Besides the semi-attached figure, there are deceptions inherent in generalized
talk about percentage increases or decreases. One of the most misleading statements
in relation to getting public support for tax cuts was US President Bush’s statement
in February 5, 2001 that “the bottom end of the economic ladder receives the biggest
percentage cuts.” This sounds very beneficial to the bottom end, but when you think
about the actual figures involved, you realize that a person who receives a tax reduc-
tion of $50 from $100 is indeed getting a 50 per cent reduction, and a person whose
taxes are reduced from $100,000 to $75,000 is indeed receiving “only” a 25 per cent
reduction, but how paltry is the benefit to the first and how generous to the second!63
3. The One-Dimensional Figure. Pictorial representations of increases or decreases can be misleading if what is true in one dimension is presented pictorially in a way that
suggests a two-dimensional or even three-dimensional situation. So, if moneybags
are used to indicate an increase of 100 per cent or double, it is misleading to present
one moneybag as having twice the height and breadth of the other moneybag since
you would in that way get the representation of an area increase with the suggestion of a volume increase (in our imaginations) following from such a doubling. But doubling the linear measurement of the sides of a square (consider a square to simplify
matters) gives an area four times the original area; for the volume, the increase is to
the cube of the linear increase. In other words, the impression created by the volume
representation is 23 or eight times the original quantity, while the actual increase was
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only double—a fourfold exaggeration. The same is true, but in the other direction, of
representing a linear decrease by a half as a volume decrease. An example of just such
a misleading impression was published in the Ottawa Citizen on December 10, 1989
when student enrolment figures were in question, and quantities were expressed by
images of schoolchildren.
Though all three graphs indicate the same 100% increase, the middle and
rightmost graphs imply greater increases due to their expansion in two and
three dimensions, respectively.
4. The “Gee Whiz” Graph. A graph can be presented in a way to make it seem as if
little change is occurring or, on the contrary, that big changes are happening. To get
the first effect, the graph starts at zero; to get the second, it begins at a base number
close to where the increase takes place. A revenue increase of $5 million plotted over
a 12-month period will look small if the starting revenue was $100 million and the
graph starts at zero and ends at $120 million. On the other hand, if the graph starts at
$95 million and ends at $110 million, the climb will look much steeper and healthier.
The picture of an institution can be put in a very different perspective by choos-
ing the base year for comparison with present happenings. If a particularly bad year
in the past is chosen, the current situation can look good by comparison. On the
other hand, if a particularly good year is chosen, the reverse can appear to be the case.
To avoid false imp
ressions, the whole situation should be set out, but institutional
managers have a strong desire to project figures in a way that minimizes their errors
and maximizes their successes. It is reasonable to suppose that the more alert the
general public becomes to possibilities for misrepresentation, the more risky such
misrepresentation will become, with the result that there will be a disincentive to
engaging in the practice.
As well as the deceptions pinpointed by Huff, there are other ways in which sta-
tistics can be manipulated.
1. Fabrication of Data. One notorious scientific fraud of the twentieth century
attempted to link intelligence to social class and heredity. Sir Cyril Burt, considered
an eminent psychologist in Britain at the time, influenced government policy with his
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findings. In a famous paper, “Intelligence and Social Mobility,” he argued that the class system was an economic result reflecting genetic ability. Professor D.D. Dorfman of
Iowa pointed out that the figures in one of Burt’s studies, which compared the intel-
ligence of 40,000 pairs of fathers and sons, matched a normal distribution so closely
as to be statistically most improbable, particularly so since other studies involving
Intelligence Quotients (IQ’s) have produced asymmetric, non-normal distributions.
In other words, the overwhelming probability is that Burt concocted his figures.64 (In
its more precise sense “normal distribution” means a distribution according to a math-
ematical formula devised by the mathematician K.F. Gauss, resulting in a bell-shaped
curve on a graph. Exact replication of this formula in nature is unlikely, although
approximations are common.)
2. Misinterpretation of the Significance of Bell Curve Differences at the Extremities.
John Allen Paulos has drawn attention to features of bell-curve distribution that
could mislead people on the alert for examples of discrimination. He notes that if
two groups, A and B, are such that one group varies slightly from the other, say in
having a mean height of 5’8’’ in one group and 5’7’’ in the other, then the two normal
curves drawn to represent height distribution among members of each group will
show a little difference in the middle of the curve, where the bulk of both popu-
lations are to be found, but differences will be accentuated at the outer edges of
the curve. Perhaps 90 per cent of those over 6’2’’ will be found in the group with
the slight height increase over the other.65 Similarly, we should not be surprised if,
where tests are done to establish job promotion potential, a group that performs
only slightly worse than another may find that significant differences are to be found
at the upper levels in the corporation because of the nature of normal distribution
curves. However, complaints about racial or other bias may still be well-founded. The
point is that finding disproportionate numbers of one group at the top level does not
of itself prove discrimination.
3. Psychological Availability Errors. Paulos also draws attention to psychological literature showing how our evaluations of people based on ambiguous news items can be
affected by words prominent in our thinking prior to examining the news items. For
example, people asked to memorize a collection of words including “adventurous,”
“self-confident,” “independent,” and “persistent” were more likely to give a positive
evaluation of a young person described in the news items than were another group
who had been asked to memorize “reckless,” “conceited,” “aloof,” and “stubborn.” The
prominence given in the media to the killing of a police officer is likely to cause the
event to register more forcibly in the minds of people than the deaths of construction
workers, so that a disproportionate number of police killings is likely to have been tal-
lied in people’s minds than deaths of construction workers. This leads to the idea that
police work is riskier than construction work, though the opposite is the case.
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When certain judgments come readily to mind because we are primed to make
them having some fresh reminder of a particular way of viewing things, then we are
under the “availability” influence. Paulos refers to a poll where 80 per cent of the
respondents said that laws should be passed to eliminate all possibilities of special
interests. The wording was altered to: “Should laws be passed to prohibit interest
groups from contributing to campaigns, or do groups have a right to contribute to the
candidate they support?” Only 40 per cent said yes. Presumably the presence of an
opposing view in the question meant that this other perspective was more available to
the respondent. “When and in what company a story breaks ... greatly influences our
perception of it,” Paulos observes, “and this is largely a matter of luck.”66 In the next
chapter some examples of the manipulative use of this feature of our perception will
be described. For the moment, it is worth taking note of Paulos’s recipe for avoiding
or reducing these influences on our thinking: we should actively strive to search for
interpretations or associations that undermine the prevailing one.
Paulos mentions two related ideas. The first is the “halo effect,” or the tendency
to upgrade our evaluation of a person or group in all categories if we are particularly
impressed by one category. The other is the notion of “anchoring effects.” If people are
asked to make an estimate when they have no real knowledge—say, about the popu-
lation of Turkey—how they will answer depends on what number is first suggested
to them. “Of those who were first presented with the figure of 5 million, the average
estimate was 17 million; of those first presented with a figure of 65 million, the average
estimate was 35 million.”67
A more difficult concept to understand is what Paulos calls “conditional probabil-
ity,”68 yet it is very important to do so if we are to have an adequate understanding of
certain forms of risk. Risk can sometimes be exaggerated for propaganda purposes. As
one saying has it, “funding follows fear.” The saying is used to debunk activist groups,
but it is also true that sales of some services or products (e.g., pharmaceuticals) can
also be increased by fear.
Suppose, Paulos continues, there is a test for a disease which is 99 per cent accu-
rate; if you have the disease, the test will give a positive result 99 per cent of the time;
if you don’t have it, it will be negative 99 per cent of the time. Consider, then, a case
where a disease has a general frequency of only 0.1 per cent, or one person in 1,000.
What will happen if 100,000 people are given the test? Statistically, there should be
100 people who have the disease, but what will the tests show?
Of the 100 people who have the disease, one will be shown not to have it, and
the other 99 will be shown to have it. But of the other 99,900 people, 1 per cent, or
999, will be shown (falsely) to have the disease. The total number of people shown
/>
to have the disease will be 99 + 999 or 1,098. So, if you tested positive, there is still
only a fairly small chance—99/1,098, or a bit over 9 per cent—that you have the
disease, despite the fact that the positive test is 99 per cent accurate for those who
have the disease.
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ConCLUSIon
The fallacies and devices discussed in this chapter are not all equally suitable for per-
suasive purposes, nor are they anywhere near a complete list. Some rhetorical and
other persuasive techniques have been, and will be, discussed elsewhere (see, for
example, Chapter 5) and are left out here merely to avoid repetition.
notes
1 Richard Crossman, “The Creed of a Modern Propagandist,” in A Psychological Warfare Casebook, ed. William Daugherty (Baltimore, MD: Johns Hopkins Press, 1958) 38.
2 Associated Press, Washington, September 29, 2001. The stated source was US government officials, including Attorney General John Ashcroft. While I have no evidence upon which to disbelieve this story, I would also note that it is consistent with a pattern of news reporting that has ignored the genuine injustices contributing to the motivations of al-Qaeda, as formulated by the presumed leader, the late Osama bin Laden.
Reference to virgins awaiting the terrorists conveniently sidesteps reflection on more serious motivations for the attacks. As UK Independent reporter Robert Fisk has remarked on more than one occasion, journalists in the mainstream media have been discouraged from raising questions about possible causes and reasons for the attack.
3 This anecdote was told by Jacintha Buddicom, “The Young Eric,” in The World of George Orwell, ed. Miriam Gross (London: Weidenfeld and Nicolson, 1971) 2, and is cited in Crick, 88–89.
4 Manvell and Fraenkel.
5 Walter Lippmann, Public Opinion, (New York: The Free Press, 1965) 81.
6 “Soldiers Al ,” Punch, March 10, 1915.
7 George Lakoff, The Political Mind (New York: Penguin Books, 2009) 75 ff.
8 Dwight Bolinger, “Truth Is a Linguistic Question,” Language 49, no. 3 (1973): 543f, crediting Julia Stanley for the first example and Donald Smith for the idea of experiencer deletion.
9 Stanley uses the different terminology of “passive adjective” to make the same point.