Misleading Statistics Companies and media often manipulate and
skew certain statistics to their advantages in order to deliver
their messages more convincingly. Because there are many ways of
presentation of statistics, it is quite easy to manipulate the
information in a misleading way. If the statistics include
surveying, a proper way of selection of population is important
(Simple Random Sampling, Clustered Sampling, Stratified Random
Sampling, and etc.). We all must be aware of these misleading
graphs and in what forms they are presented to us, and be able to
analyze, and fix such graphs so that they are no longer misleading,
to the benefit of our society.
Slide 3
Two different bar graphs are made from the same survey of
favorite foods:
Slide 4
The same information can be accurately presented in a
non-misleading way : If we take the same information and present it
in a pie graph, we can see the more accurate result of the survey.
Unlike the previous graph which depicted hot dogs as the favorite
food by misrepresenting the origin on the y-axis, this pie graph
shows that all three foods are equally preferred, a more realistic
result.
Slide 5
Comparative Causes of Annual Deaths in the United States
Provided by CDC Certain crucial information are missing. There is
no way for us to know whether or not CDC has counted smokers who
have died from diseases or accidents. There is a good chance that
any smoker that died from a disease has been counted as those that
died from smoking. Here is a question to ask the CDC: A simple
glance at this graph will make us conclude that smoking is the
leading cause of death among Americans. However, an in-depth
analysis of this graph will easily tell us that it is greatly
misleading. A person who smokes has died from a heart disease. What
was his cause of death?
Slide 6
Ways to fix misleading graphs - I One way to fix a misleading
graph is to present in a different way, like what we have done for
the previous information(favorite foods). However, it seems there
is no significant change in the information even after we have made
a pie graph from the initial bar graph. We now have to question the
method of construction of the graph by the CDC.
Slide 7
Ways to fix misleading graphs - II - How the CDC has collected
their data is very doubtful. The graph does not provide any
information about the number of deaths caused by smoking. If
smoking is not the primary cause of death, then it should not be
the cause of death. - The CDC may say that 418,000 people who have
died were smokers, but they cannot say that they have died because
of smoking. - The graph presented on the next slide is a more
accurate graph regarding the causes of annual deaths in the United
States:
Slide 8
Revised Graph Percentage of Smokers in Each Cause of Annual
Death in the United States
Slide 9
Analysis of the Revised Graph From the revised graph, we can
tell that certain percentages of people who have died from each
disease smoked. This graph does not imply that smoking is the
leading cause of death in the United States. It does, however,
imply that smoking contributes to deaths in the United States. For
instance, we can assume that smoking is closely related with cardio
vascular diseases such as heart disease and cancer, for chemical
included in a cigarette such as tar is able to block blood vessels,
ultimately causing heart diseases. We can also assume that smoking
is intimately related to deaths cause by usage of drugs. We cannot
draw a fact from most statistics. It is important to conduct the
survey and the construction of presentation as in the most
realistically accurate, reliable, and non-misleading way as
possible, and the conclusions drawn from the presentation, must not
be general, but acutely specific.
Slide 10
Price Per Barrel of Light Crude Oil Leaving Saudi Arabia on
Jan. 1 The pictograph on the left indicates the amount of increase
in crude oils in transport from Saudi Arabia. The ratio of the size
of the barrel to the actual price is not in proportion. The
difference in sizes of the barrels are conveyed to exaggerate the
increase or decrease in the price of a barrel of crude oil. It is,
moreover, hard for readers to visually compare prices in each year.
Therefore, this pictograph is potentially misleading.
Slide 11
Revised Graph Instead of using barrels with different sizes to
describe the increase in prices, a properly constructed bar graph
would present the information more accurately.
Slide 12
Revised Graph - II - Another adequate way of fixing the graph,
showing the gradual increase in the oil prices effectively through
a line graph.
Slide 13
Chevy Advertisement This is a misleading graph to serve a
purpose which is to indicate that Chevy is the most preferred car
among people, thus possibly persuading many others to purchase
Chevy. However, if we look at the graph closely, it can be seen
that the y-axis does not start at zero. The viewer of this graph
may take this misleading graph for how it looks, and will procure a
false and inaccurate information. In order to fix this misleading
graph, we would have to possess a precise and accurate information
with which we could organize a properly designed graph. The y- axis
of the graph must also begin from 0, in order to display an
accurate comparison. Without sufficient information, we cannot but
simply be aware that graphs such as this are misleading because of
their obscurity of the origin on the y-axis.
Slide 14
What makes some statistical information accurate and reliable?
Statistics is a set of methods that are used to collect and analyze
data. Because it is used to help many people to make good decisions
about uncertain situations, many people tend to believe any
statistic that is presented to them by a company. However, as you
have seen through our presentation, statistics are very easy to
manipulate; without an adequate understanding and analysis of the
statistical information, it is easy for us to take misleading
statistics seriously. Accurate and reliable statistics come from
proper procedure of defining the problem, collecting the data,
analyzing the data, and reporting the data. These 4 procedures must
be done rationally and as accurately as possible, in order to
prevent the statistics from becoming misleading. We will explain
the adequate ways to conduct the 4 procedures, and ultimately to
make accurate and reliable statistics.
Slide 15
Defining the Problem Every word in a statistical problem must
be defined extremely specifically and accurately. For example, if
the problem was counting the number of inhabitants of Kerrisdale,
Vancouver, on a specific date, we would have to define inhabitants
to know who to count into the survey. Also, Kerrisdale must be
defined specifically in order to decide where to stop the survey.
Factors such as newborn babies in the hospital must be taken into
consideration. If one of these pieces of information is not clearly
define, it would be extremely difficult to begin gathering
data.
Slide 16
Collecting the Data For each kind of problem, different
information is needed, and so is the method of collecting the data.
One of the most important parts of establishing a statistic is to
design an effective way of collecting data. We collect data from a
population or from a sample. When the population of the survey is
selected from a sample, the selected population must be able to
provide exactly required information for the purpose of the survey.
The most exacting and informative form of data collection for
comparisons is randomized controlled experiment. The population is
divided into randomly separated groups, and are selcted
randomly.
Slide 17
Analyzing the Data ~ Exploratory Methods ~ This method often
involves a lot of calculating averages and percentages, and
displaying the information on a graph. Although Exploratory methods
may provide many pieces of information, it may not answer specific
questions or make definite statements about a problem. ~
Confirmatory Methods ~ This method is used to conclude the results
of the survey and the statistical information by answering specific
questions. For example, using a confirmatory method, a statistician
can say Oil Prices leaving Saudi Arabia has been increasing, and
will increase in prices. Not one of these methods should be
overlooked. Both methods should be used extensively to analyze the
results of a statistical activity and will have to come to
varieties of extremely specific conclusions with credibility and
accuracy.
Slide 18
Reporting the Results Inference is used to draw conclusion from
a statistical activity; even from a small collection of
observations or experimental results, careful and rational
inference can create an accurate and reliable generalization that
can be used to used to the social benefits. There are many forms of
presentations, and they include bar graphs, pie graphs, tables, or
a set of percentages. However, when drawing conclusions, one must
take into consideration the fact that the survey was carried on a
specifically selected sample population, not the entire population.
Therefore, using probability, the conclusions must reflect and
include the uncertainty possibly excluded or misrepresented in the
statistics.
Slide 19
How We Would Conduct Statistical Activities Everything that has
been presented to you by the previous slides must be considered
when carrying out a statistical activity. When everything is
carefully done, the statistics will be truly accurate and reliable.
Thank you for viewing our presentation!
Slide 20
Bibliography Fienberg, Stephen E. Statistics. The World Book
Encyclopedia. 2002 ed. Goodman, Jeff. Math and the Media:
Deconstructing Graphs and Numbers. Jeff Goodman. Modification Date:
N/A Appalachian State University. Access Date: 1 December 2003.
Knox, Pattie. "Excel Activities for the Classroom. North Canton
City Schools. Modification Date: N/A Access Date: 1 December 2003.
Misleading statistics by the CDC. Jeremiah Project. Modification
Date: 21 May 2003. Access Date: 1 December 2003.