Opinions to Shape Statistics
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“Every year since 1950, the number of American children
gunned down has doubled.” 1
This statistic may shock you and make you question the security
we provide for our children, but there is one problem: it is not true. If
you carefully analyze this statement you would realize that if this
statement was accurate, the number of American children killed by guns
in 1995 would be 35 trillion even if the number killed in 1950 was one.
Clearly, you would then realize that the number of children killed each
year could not be nearly 4400 times the size of the world’s population. If
you simply looked at this statement and did not think deeply about what
it was literally saying, you may accept it as the truth. This appeared in a
newspaper article and was quite different from the original data. The
original statistics, provided by the Children’s Defense Fund, stated the
number of American children killed by guns each year has doubled since
1950. 1 This simple difference in wording provides a much more powerful
statement that is actually completely false.
These statistics shape our perceptions and alter our decision
making process. Statistics like these appear everywhere in our world.
You can find them in newspapers, magazines, reports, and many other
places. This global display of false numerical claims raises questions about
the ethics of statistics and what is expected of the people providing these
In this paper, I will explain the various ways in which statistics can
be flawed, the ethics involved in these misrepresentations, and possible
ways to limit the power of misleading statistics. I will examine the ethics
from duty-based perspective, and discuss the obligations of both the
presenters of the information and the audience using that information to
Prior to discussing anything further on statistical manipulation, we
must first examine the human response to statistics. For almost any
argument, statistics are employed to represent facts. An exploration into
the definition of statistics, as expressed by early statisticians, returns a
common idea that statistics are “numerical statements of fact”. 2 When
people see statistics, they tend to believe the numbers are sound and
were reliably collected. 3 It is clearly seen that people trust statistics
simply by looking at the wide range of areas in which they are applied.
Statistics are used to make decisions in government, the economy,
science, medicine, and even in our own personal lives. 4 If we continuously
use statistics to make important decisions in our society, should we not
question whether statistics represent concrete facts? Since statistics help
drive critical decision making, it is important to not be making conclusions from anything other than actual facts. A careful examination of all the
processes involved in collecting and compiling statistics is required in
order to fully understand why this data should not be merely accepted as
Uses of Statistics
We must first establish why the ethics of statistics is a relevant
topic. Even by viewing the material of an introductory statistics class, one
can understand the wide array of uses for statistics. Surveys are a major
source of statistical data. They are used in dozens of different areas.
Government agencies use surveys to determine the amount of
unemployment and to establish the Consumer Price Index (CPI). The CPI
is a major economic indicator, which can be used to evaluate the
effectiveness of an administration’s economic policies. 5 Statistics are also
commonly used to determine to what extent a company is financially
stable. This data helps guide if an individual should invest in particular
Statistical studies are used as the basis for making decisions in
several other areas. Companies use surveys to conduct marketing
research to help determine what customers want to buy. Sociological
research can be done by surveying people to understand the way people
live and the way society is constructed. 6
In education, schools are judged based on the statistics of their
students test scores. Funding can be largely based on these numbers.
Thousands of schools can be affected if false data is used. Studies are also
often used in medicine to determine the effectiveness of a drug and its
possible side effects. The implications flawed data can have on the users of these drugs are enormous. An unsafe drug could reach the market if
incorrect data showed it was safe. They also use statistics to determine
the important risk factors that can lead to contracting a certain disease.
Accurate numbers can help guide doctors into testing for diseases for
which a patient is more likely to contract.
From these few examples taken from the thousands of uses for
statistics, it is clear that the accuracy of statistics used in decision making
is truly an issue. With so many key choices being dependent on what the
numbers tell us, it is important to consider the ethical uses of these
numbers and the effects misleading statistics can have.
Lying with Statistics
The term lying leads many to think that someone is purposely
attempting to deceive them. In order to fully understand how statistics
can be misleading, one must realize that people can accidentally present
statistics that misrepresent the actual data. 7 Before considering the
ethics associated with statistics, we must understand these two broad
areas of statistical misinformation. It also must be noted that since
accidental and intentional misrepresentations are quite different, the
ethical examinations should be done separately.
When evaluating the accuracy of statistics, one must look at the
creation process. Data is collected, interpreted, and then presented.
Mistakes can be made at all levels of construction. It is important to - 44 -
understand the many types of errors that can occur in order to realize
how easily statistics can be flawed.
The most common errors in statistics are known as sampling
errors. 8 When statistics are collected, the entire population is not usually
included in the test. Instead, a sample is taken which is supposed to be
indicative of the entire population. It is clear that errors can arise because
the characteristics of a smaller portion of a whole do not always exactly
represent the characteristics of that whole. By using probability sampling
methods, it is possible to estimate the amount of sampling errors, but
probabilities are not perfect. Sampling error can be reduced by using
larger samples and also by using effective methods to select the samples.
In all studies, it is accepted that the information has a certain amount of
unreliability. The main problem, though, is that this amount of
unreliability is not usually stated when the statistics are displayed. The
audience is unaware of the possibility of inaccurate data.
It is important to understand that numbers must be examined in
context. Many make the mistake of comparing just raw numbers and not
really taking into account the specific situations surrounding those
numbers. 9 If one was to compare the number of police officers in Los
Angeles to the number in Anchorage without considering the population
difference, it is easy to make the claim that Los Angeles is safer than
Anchorage. The raw numbers simply do not tell the entire story and thus
any conclusions drawn from just those numbers could be faulty.
One of the main concerns involved during the collection stage of
statistical analysis is the likelihood of bias. 10 Again, we look at the idea of
samples. The people conducting the surveys are in control of selecting
what to include or who to include in the collection. If this group intends
to prove a particular point, it is clearly seen that they might be drawn to - 45 -
samples that would be more likely to present figures to support their
position. It is important to note that this is not always the intent, but it is
almost impossible to conduct a survey without some bias.
Another problem with the people in charge of the surveys is that
many times these people do not have a strong knowledge of the subject
matter. 11 If someone does not understand what they are working on, it is
hard to be certain that the important data is being collected and
displayed. You would not want someone who does not have a strong
understanding of medicine and diseases to being testing drugs to help
Ethics of Flawed Data
As stated before, I will analyze this from a deontological or duty-
based perspective. Mostly based on the ideas of Immanuel Kant, this
theory suggests that our morals are based on the obligations we have to
each other. 12 Every action is basically subject to a universal moral law
which promotes treating individuals as ends in themselves rather as
means to an end. By this logic, everyone would treat everyone else based
on standard rules, and thus all could be treated fairly. This theory does
not look at consequences because one cannot always be sure what could
result or the implications of those results.
I must mention in my discussion of mistakes that my assertion is
that making mistakes is an ethical matter. Even though one can claim that
an accidental error is not an ethical matter because it is not a purposeful
attempt to deceive, I suggest that acknowledging that errors will occur
and taking action to limit those errors is subject to ethical scrutiny. It is
widely accepted that no survey can be absolutely accurate and that there will always be mistakes. The ethical issue arises in the idea that people
have some obligations to realize the possible errors and take measures to
reduce their impact on the overall survey. In other words, I will discuss
whether it ethical to simply ignore the possibility of errors and take no
action to attempt to eliminate them. When analyzing the ethics involved
in making mistakes in statistical studies, we must first look at what would
be involved in ensuring these mistakes are limited. First, exploring errors
made in displaying the statistics, it certainly seems that more effort could
be made to have data shown accurately. From a duty-based perspective,
statisticians and those using statistics have a duty to attempt to provide
the most accurate information. Based on this duty, it is unethical to cut
corners and not attempt to display information in the most accurate way
possible. In displaying, it is simply a matter of selecting an accurate way
to show the particular statistics. It may take a little more time and
research to find the best way to display the data, but it is necessary to
uphold the duty to the audience.
Now it is important to consider the problems with data collection
differently than the display of that data. The data collectors still have the
same duty to attempt to produce the most accurate information, but they
are limited in terms of collection. They should attempt to get the largest
possible sample and the one that is most comparable to the population. 13
They may be limited by the cost of collecting larger samples, but again I
emphasis they must attempt, to the best of their ability, to reduce errors.
I will not claim that there should be a specified size of a sample, but based
on the constraints of each individual situation, one could determine the
largest possible sample. Even with this though, it would be impossible to
eliminate all bias and sampling errors. To act ethically, their goal should
just be to limit the amount of errors. They clearly have a duty to select qualified people to conduct the studies. It may cost more to hire experts,
but that is the only way to ensure the most important data is being given
the most attention and possible mistakes made out of ignorance are limited.
If they cannot afford to qualified surveyors, the ethical thing to do may be
just not to conduct the survey at all. If the accurateness of the survey is
compromised, it will really not serve its purpose and will not really be useful
in decision making.
Bending the Numbers
Ethics in statistics becomes even more of a concern when you
examine the ways people use statistics to intentionally deceive their
audience. People want the statistics they provide to help prove the argument
they are trying to make. 14 This desire may drive some to manipulate their
data to lead to certain conclusions. I will break intentional misuse of statistics
into three basic categories: manipulation of raw data, displaying data in a
misleading way, and completely omitting data.
There are many ways people can lie with statistics. One obvious way
would be to alter the data or simply make up the data all together. 15
Someone can do a study or claim to do a study and then present some
numbers. These numbers could have no truth behind them, but since people
often accept statistics as hard facts without question5
, 16 this type of practice
has a good chance of actually obtaining its desired results.;
When we first discussed bias, we only looked at people accidentally
being influenced. People can also purposely attempt to steer data. If
someone believes deeply in a cause, that person may purposely select data
that would best support that cause. The data itself is correct for the specific
sample, but most likely does not accurately represent the entire population.
In the case of surveys, the interviewer could manipulate the data by
manipulating the test subject. They could change the way they form their
questions or the way they ask questions in order to lead the subject to a
certain conclusion. In this way, the data is actually the data that was
collected, but still would not present the truth.
It is clear that data can easily be manipulated and there are a really
no sure ways to prevent it. Laws really can’t do much to stop people from
fabricating data, so ethical thought is the only way to really look at this
tatistics can be misleading because of the way they are displayed.
The data may be accurate, but there is still an attempt to be deceptive.
Display methods can easily deceive the audience. In Figure 1 below, simply
changing the scale from 0-250 to 100-215 gives a completely different idea
about the number of police in each city.
There are several other ways to make data appear to say different
things. The way things appear visually to us has a real impact on our
opinions. In the second graph it appears that City 2 has twice as many police
officers as City 1, but looking at the first graph, you can tell that is
incorrect. Deception can occur based on how the information is
Another way people can lie with statistics is by omitting them. 17 A
prime example would be with the drug company Merck. 18 They
developed a drug for treating arthritis called Vioxx. Prior to submitting
this drug to the public, they conducted a series of tests that showed that
it had a strong correlation to increased heart attack risk. Merck
proceeded to rush the drug to market and never included any information
to the public about the heart attack risk. The data Merck obtained in their
study would have had a negative effect on selling their drug and thus they
simply chose to omit some very important information. This is misleading
because Merck had the data showing the heart attack risk, but since they
omitted that data, people have a false sense that there is no increased
heart attack risk.
There are many reasons why people choose to manipulate
statistics. They may feel pressure from outside sources, they may be
constrained by budget, or they may have personal objectives or values
they wish to support. 19
To understand the dilemma of statistical manipulation it is
important to see that good can come out of statistical manipulation. In
the case of the drug Vioxx, many people could benefit from the drug’s
positive effects. By omitting some data, Merck was able to get the drug
into the market for the people who needed it. They may have believed
that the studies they did were valid, but the positives of the drug
outweighed the increased heart attack risk. Thus, by misleading their
audience, they were able help thousands of people.
I would contend though, that even if the drug caused no heart
attacks in the population, Merck did act unethically. Merck conducted a
study and had a duty to provide the results of that study. Ethically, no
one should ever manipulate data, even if they have good intentions and it
could lead to a favorable outcome. First, you have to consider who would
decide what a good outcome is. A good outcome for one group of people
is not always a good outcome for another. Even if you ignore that fact,
and we hypothetically say that everyone agrees on what is a good
outcome, you could still not argue for manipulation based on good
intentions. You could not universally apply some sort of maxim that
suggested that you should manipulate data if it can lead to good results.
The very practice of statistical analysis would be useless. If everyone
simply changed factual data to support their cause or even just left out
the data against it, all data would loss any meaning it could have had. In
order for statistics to actually be a useful, factual tool, statisticians must
consistently present the genuine data.
Data manipulation can in no way be ethical. Statisticians have a
duty to present the accurate and complete results of their studies.
Accepting any sort of manipulation means accepting all manipulation,
good and bad.
Proper use of statistics and making decisions based on statistics is
the responsibility of both the people supplying the statistics and those
using them. The statisticians have a responsibility to provide the most
accurate information possible. We have already discussed their ethical
responsibility pertaining to intentional manipulation and also that they
must be required to reduce their mistakes. It is their responsibility to
study the mistakes they made and improve their statistical system. 20
There are many ways to ensure that data is accurate as it can be. They
can look at other similar studies that have been successful in using
appropriate methods and learn how best to conduct their own study.
They can do the research multiple times with different samples. Some
methods may not be cost effective, but there is always a way to better
One must know that it is also the viewer’s job to determine how
to use the statistics he is presented. Audiences need to be aware of the
possibility that the statistics they are seeing may not actual be
representative of the truth. It is important to analyze data rather than
just accepting it as the truth. The audience also has a duty to make well-
informed and conscientious decisions. To do this, they must take certain
steps to analyze the validity of statistics. First, when viewing statistics,
they must step back and look at the data as impartial observers. Humans
tend to confront statistics that question our beliefs and are more forgiving
of those which support them. 21 We need to consider the issue of
construction. Before we accept a statistic, we must analyze who is giving
us this statistic, where they got their information, and what methods they
used to get it. 22 Understanding these things will help us understand possible biases and other problems associated with the stats. The main
thing to remember is not to simply accept statistics as fact.
If we simply look deeper into statistics, we can weed out false and
misleading information and be able to have a more informed perspective.
So remember this the next time you see something like this:
“In a study in 1685 of the ages and professions of deceased men, it was
found that the profession with the lowest average age of death was
‘student.’ Being a student seems like a very dangerous occupation.” 23
Examine this statement closely and now you should be able to
understand why we should think about what we read or we might just
jump to some absurd conclusions.
1. Best, Joel. (2001). Damned Lies and Statistics. Berkeley: University of
2. Annadurai, B. (2007). A Textbook of Biostatistics. New York: New Age
3. Best, Joel. (2005). Lies, Calculations and Constructions: Beyond How to
Lie with Statistics. Statistical Science, 20, 210-214.
4. Ibid 2
5. U.S. Bureau of Labor Statistics. (2001). Consumer Price Index. BLS.
Retrieved November 19, 2007, from http://www.bls.gov/CPI
6. Wild, Chris and George Seber. (1999). Chance Encounters: A First
Course in Data Analysis and Inference. New York: John Wiley and Sons.
7. Gelman, Andrew and Deborah Nolan. (2002) Teaching Statistics: A Bag
of Tricks. New York: Oxford University Press.
8. Groves, Robert. (2004). Survey Errors and Survey Costs. New York:
9. Ibid 7
10. Ibid 7
11. Jaffe, A.J. (1987). Misused Statistics: Straight Talk for Twisted
Numbers. New York: Marcel Decker Inc.
12. Kant, Immanuel. (1997). Groundwork of the Metaphysics of Morals.
New York: Cambridge University Press.
13. Arnold, Margery. (1996). The Effects of Two Types of Sampling Error
on Common Statistical Analyses. New Orleans: Southwestern
Educational Research Association. (ERIC Document Reproduction Service
14. Huff, Darrell. (1954). How to Lie with Statistics. New York: Norton.
15. Ibid 7
16. Ibid 5
17. Ibid 10
18. Testimony of David J. Graham, MD, MPH, November 18, 2004.
Associate director for Science and Medicine in the Office of Drug Safety,
19. Seltzer, William. (5 Feb. 2001). U.S. Federal Statistics and Statistical
Ethics: The Role of the American Statistical Association’s Ethical Guidelines
for Statistical Practice. Washington Statistical Society Seminar: Washington.
20. Seltzer, William. (2005). Official Statistics and Statistical Ethics:
Selected Issues. New York: International Statistical Institute.
21. Ibid 3
22. Ibid 3
23. Ibid 7