A Field Guide to Lies: Critical Thinking in the Information Age (32 page)

Modus ponens.
A valid type of deductive argument of the form:

If A, then B

A

Therefore, B

Post hoc, ergo propter hoc
(after this, therefore because of this).
A logical fallacy that arises from thinking that just because one thing (Y) occurs after another (X), that X
caused
Y. X and Y might be correlated, but that does not mean a causative relation exists.

Precision.
A measure of the level of resolution of a number. The number 909 is precise to zero decimal points and has only a resolution of the nearest whole number. The number 909.35 is precise to two decimal places and has a resolution of 1/100th of a unit. Precision is not the same as accuracy—the second number is more precise, but if the true value is 909.00, the first number is more accurate.

Prevalence.
The number of existing cases (e.g., of a disease).

Scatter plot.
A type of graph that represents all points individually. For example, opposite is a scatter plot of the data presented
here
.

Subdividing.
Breaking up a set of observations into smaller groups. This is acceptable when there is heterogeneity within the data and the larger group is composed of entities that vary along an important dimension. But subdividing can be used deceptively to create a large number of small groups that do not differ appreciably along a variable of interest.

Syllogism.
A type of logical statement in which the conclusion must necessarily follow from the premises.

Truncated axis.
Starting an x- or y-axis on a value other than the lowest one possible. This can sometimes be helpful in allowing viewers to see more clearly the region of the graph in which the observations occur. But used manipulatively, it can distort the reality. The graph shown in this glossary under the entry for “scatter plot” uses two truncated axes effectively and does not give a false impression of the data. The graph shown
here
by Fox News does give a false impression of the data, as shown in the redrawn version
here
.

NOTES

INTRODUCTION: THINKING, CRITICALLY

avoid learning a whole lot of things that aren’t so
:
After Huff, D. (1954/1993).
How to Lie with Statistics
. New York: W.W. Norton, p. 19. And, as you’ll read later, he probably was echoing Mark Twain, or Josh Billings, or Will Rogers, or who knows who.

Misinformation has been a fixture of human life
:
Abraham provides misinformation about the identity of his wife, Sarah, to King Abimelech to protect himself. The Trojan horse was a kind of misinformation, appearing as a gift but containing soldiers.

PART ONE: EVALUATING NUMBERS

People choose what to count
:
This sentence is nearly a direct quote from Best, J. (2005). Lies, calculations and constructions: beyond
How to Lie with Statistics.
Statistical Science, 20
(3)
,
210–214.

More people have cell phones than toilets
:
Wang, Y. (2013, March 25). More people have cell phones than toilets, U.N. study shows. http://news feed.time.com/2013/03/25/more-people-have-cell-phones-than-toilets-u-n-study-shows/.

150,000 girls and young women die of anorexia each year
:
Steinem, G. (1992).
Revolution from Within.
New York: Little, Brown. Wolf, N. (1991).
The Beauty Myth.
New York: William Morrow.

Add in women from twenty-five to forty-four and you still only get 55,000
:
This example came to my attention from Best, J. (2005). Lies, calculations and constructions: beyond
How to Lie with Statistics.
Statistical Science, 20
(3)
,
210–214. The statistics are available at www.cdc.gov.

anorexia deaths in one year cannot be three times the number of
all
deaths
:
Maybe you’re in the accounts payable department of a big corporation. An employee put in for reimbursement of gasoline for the business use of his car, $5,000 for the month of April. Start with a little world knowledge: Most cars get better than twenty miles per gallon these days (some get several times that). You also know that the fastest you can reasonably drive is seventy miles per hour, and that if you were to drive ten hours a day, all on the freeway, that would mean 700 miles a day. Keep that up for a standard 21.5-day work month and you’ve got 15,050 miles. In these kinds of rough estimates, it’s standard to use round numbers to make things easier, so let’s call that 15,000. Divide that by the fuel economy of 20 mpg and, by a rough estimate, your employee needed 750 gallons of gas. You look up the average national gas price for April and find that it’s $2.89. Let’s just call that $3.00 (again, rounding, and giving your employee the benefit of the doubt—he may not have managed to get the very best price every time he filled up). $3/gallon times 750 gallons = $2,250. The $5,000 on the expense report doesn’t look even remotely plausible now. Even if your employee drove twenty hours a day, the cost wouldn’t be that high. https://www.fueleconomy.gov/feg/best/bestworstNF.shtml, retrieved August 1, 2015. http://www.fuelgaugereport.com/.

a telephone call has decreased by 12,000 percent
:
Pollack, L., & Weiss, H. (1984). Communication satellites: countdown for Intelsat VI.
Science, 223
(4636), 553.

one of 12,000 percent seems wildly unlikely
:
I suppose you could spin a story that makes this true. Maybe a widget used to cost $1, and now, as part of a big promotion, a company is not just willing to give it to you for free, but to
pay
you $11,999 to take it (that’s a 12,000 percent reduction). This happens in real estate and big business. Maybe an old run-down house needs to be razed before a new one can be built; the owner may be paying huge property taxes, the cost of tearing down the house is high, and so the owner is willing to pay someone to take it off of his or her hands. At one point in the late 1990s, several large, debt-ridden record companies were “selling” for $0, provided the new owner would assume their debt.

200 percent reduction in customer complaints
:
Bailey, C., & Clarke, M. (2008). Aligning business leadership development with business needs: the value of discrimination.
Journal of Management Development
,
27
(9), 912–934.

Other examples of a 200 percent reduction: Rajashekar, B. S., & Kalappa, V. P. (2006). Effects of planting seasons on seed yield & quality of tomato varieties resistant to leaf curl virus.
Seed Research, 34
(2), 223–225. http://www.bostoncio.com/AboutRichardCohen.asp.

50 percent reduction in salary
:
Illustration © 2016 by Dan Piraro based on an example from Huff, ibid.

making this distinction between percentage point and percentages clear
:
I’m grateful to James P. Scanlan, attorney-at-law, Washington, D.C., who answered my query to the membership of the American Statistical Association, and provided me with this misuse.

closing of a Connecticut textile mill and its move to Virginia
:
This example comes from Spirer, L., Spirer, H. F., & Jaffe, A. J. (1987).
Misused Statistics
, New York: Marcel Dekker, p. 194.

Miller, J. (1996, Dec. 29). High costs are blamed for the loss of a mill.
New York Times,
Connecticut Section
.

And n. a. (1997, Jan. 12). Correction,
New York Times
, Connecticut Section
.

legislation that denied additional benefits
:
McLarin, K. J. (1993, Dec. 5). New Jersey welfare’s give and take; mothers get college aid, but no extra cash for newborns.
New York Times
.

See also: Henneberger, M. (1995, April 11). Rethinking welfare: deterring new births—a special report; state aid is capped, but to what effect?
New York Times
.

births to welfare mothers had already fallen by 16 percent
:
Ibid.

no reason to report the new births
:
Ibid.

Although they are mathematically equivalent
:
Koehler, J. J. (2001). The psychology of numbers in the courtroom: how to make DNA-match statistics seem impressive or insufficient.
Southern California Law Review
,
74
, 1275–1305.

And Koehler, J. J. (2001). When are people persuaded by DNA match statistics?
Law and Human Behavior
,
25
(5), 493–513.

On average, humans have one testicle
:
Attributed to mathematics professor Desmond MacHale of University College, Cork, Ireland.

temperatures ranging from 15 degrees to 134 degrees
:
http://en.wikipedia.org/wiki/Death_Valley.

the amount of money spent on lunches in a week
:
As an example, suppose six adults spend the following amounts on lunch {$12, $10, $10, $12, $11, $11} and six children spend the following {$4, $3.85, $4.15, $3.50, $4.50, $4}. The median (for an even number of observations, the median is sometimes taken as the mean between the two middle numbers, or in this case, the mean of 4.5 and 10) is $7.25. The mean and median are amounts that no one actually spends.

During the 2004 U.S. presidential election
:
See Gelman, A. (2008).
Red State, Blue State, Rich State, Poor State.
Princeton, NJ: Princeton University Press.

the average life expectancy for males and females
:
These numbers are for white males and females. Non-white figures for 1850 are not as readily available. http://www.infoplease.com/ipa/A0005140.html. An additional source of concern is that the U.S. numbers for 1850 are for the state of Massachusetts only, according to the Bureau of the Census.

the average family
:
The title of this section, and the discussion, follows the work of Jenkins and Tuten very closely:

Jenkins, J., & Tuten, J. (1992). Why isn’t the average child from the average family? And similar puzzles.
American Journal of Psychology
,
105
(4), 517–526.

the average number of siblings
:
Stick-figure children from Etsy, https://www.etsy.com/listing/221530596/stick-figure-family-car-van-bike-funny; small and large house drawn by the author; medium house from http://www.clipartbest.com/clipart-9TRgq8pac.