Critical Thinking 101 –
Statistics and Deception
Gail P. Taylor, Ph.D.
MBRS-RISE Program, UTSA
References:
the Right Questions – A guide to
critical thinking. N. Neil Browne and
Stuart Keeley. Prentice Hall, 2000.
 Asking
What is Critical Thinking?
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An awareness of interrelated critical questions
that you employ at appropriate times
 Results in systemic, active evaluation of what
you read and hear
 Influences how you react to information
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Accept?
Reject?
Withhold judgment
Must also critically evaluate your OWN
conclusions…
The Way of the World
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World- There will always be topics that are up
for debate, with “reasonable” experts on both
sides
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Laboratory- There will often be more than one
interpretation for experimental results
observed
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Some “Facts” are solid (measurements)
Some more open to interpretation
Social/Psych science is particular vulnerable
Approach to Information
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Sponge
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Absorb everything…but no value judgment
Panning for Gold
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Ask about speaker motives
Actively identify possible problems with what is
being said?
Evaluate identified problems?
Form your own conclusions…
Beware Emotional Involvement
with Opinions…
 Everyone
has pre-existing opinions
 The older the opinion, the more likely
you didn’t examine it
 May have great emotional attachment to
un-examined opinions
 Do not “fall in love” with your ideas or
opinions, so that they blind you to the
truth…
In Science, Critical Thinking is
used in your own Research…

The Scientific Method itself involves critical thinking
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Observe problem/phenomenon/conceive ideas
Make Predictions/Develop a hypothesis
Devise a test/Formulate experiment
Carry out experiments
Draw conclusions from results
Reject or support hypothesis
Revamp experiment and continue onward…
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VITAL for a scientist.
Impressive for a science student
Need to take time to read and think
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…And When You look at Others’
Research Results
 Are
the ideas supported by the literature?
 Are the techniques correct?
 Was data analyzed correctly?
 Are their conclusions supported by the
data?
The “Right” Questions

What is the issue/problem?
 What are the conclusions?
 What is the supporting evidence or reasons?
 Are any significant words or phrases ambiguous?
 How good is the evidence?
 Are the statistics deceptive?
 Are there hidden assumptions?
 Are there any fallacies in the reasoning?
 What significant information is omitted?
 Are there rival causes/theories?
 Are the conclusions reasonable?
How to Find Issues
What is the Issue?

Given: They are trying to influence your beliefs

What question (or controversy) are they trying to
influence your beliefs ABOUT?

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In the “World” often about personal agendas
In Science, can be to persuade you to the validity
of their results and viewpoint/theory about a field.
Where and How to Find the
Issue:
 Often
very obvious
 Generally found at beginning
 Sometimes only implied
It’s the question being addressed
 Inferred through conclusion
 Inferred through examination of author’s
associations…

 “They
are trying to influence my view
of…What??”
Explicit Issue:
 The
question I’m raising is: Why must
we have speed limits on our highways?
Implied Issue
By now, more than two years after voters
overwhelmingly approved the lottery, it has been
proven that the game is not a success; in fact, it
can be considered a failure…
What is the author reacting to?
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Issue: What is the impact of the Lottery?
Two Types of Issues
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Sometimes difficult to discern
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Descriptive (how the world IS):
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Usually see in science
What is the molecular basis for hibernation?
Who decides to reduce the drinking age?
Do families with pets argue less frequently?
Prescriptive (How the world should BE)
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Ethical/Moral
Should we reduce the drinking age?
What ought to be done about welfare?
Conclusions
 Given:
They are trying to influence your
beliefs
 “What
are they trying to get me to
conclude?”
Finding Conclusions
 Often
at the end (but not always)
 Often accompanied by specific phrases
Finding a Conclusion
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We conclude that
Results indicate
Consequently
Hence
Therefore
Thus
In short
It follows that
Shows that
Indicates that
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Suggests that
It should be clear that
We may deduce that
Points to
The point I’m trying to make is
The most obvious explanation
It is highly probably that
Proves that
The truth of the matter is
Conclusion?
By now, more than two years after
voters overwhelmingly approved the
lottery, it has been proven that the
game is not a success; in fact, it can
be considered a failure…

Conclusion: The lottery is not a success
and is in fact a failure
Example
Divorce is on the increase, and we’re
worried. Finally, Psychologists have
identified a key cause of divorce.
Noticing that certain families have
multiple divorces, they found that
inherited genes play a major role in
causing divorces.
Although overall divorce rate is 20
percent, psychologists have
discovered that a twin has a 45
percent rate of divorce if the
identical twin has already
experienced a divorce. Additional
confirming evidence for genes as a
primary cause stems from looking a
the divorce rate of twin’s parents. If
their parents have divorced, each
twin has a 10 percent higher risk of
divorce
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Issue:
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What is the cause of Divorce?
Conclusion:
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Inherited genes are a major cause
Quick Talk about Stats!
Statistics 101
 Statistics-
Evidence expressed as
numbers
 Can and often DO lie…esp. in popular
press
 Can also seem counter-intuitive to
people…
Humans, Risk and Stats…
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Statistics may seem counter-intuitive…
 Automobile Deaths:
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1.7 deaths per 100 million veh. miles
Population risk per year: 1 in 6,300
Air Carrier Deaths:
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0.7 deaths per 100 million aircraft miles
0.19 deaths per million aircraft departures
Population risk per year: 1 in 1,568,000
http://hazmat.dot.gov/riskcompare.htm
General Strategies to Detect
Statistical Deception…
 How
were the statistics obtained?
 What are the Motivations of quoter?
 What does “average” mean?
 Are the conclusions supported by the
stats?
 Is all the information needed for
evaluation there?
How Obtained –
Unknowable Statistics
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There are obstacles to getting accurate
statistics on some topics…
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Physical barriers to obtaining information
Failure to report events
Improper sampling
Deception
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“Educated Guesses”
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Have to analyze what the person stating the
stats has to gain….
Is there a truly a perfect way
to find out the following?
 Number
of Aids cases?
 Number of Abortions?
 How many people shoplift?
 Have affairs?
 Have a mental disorder?
 Use cocaine?
 Commit white-collar crimes?
 Are homeless?
 Beat their wives?
Biased Statistics – Bad Initial
Sampling…
 We
randomly polled 500 people from
California, Florida, and Maine and have
concluded that 34% of Americans prefer
to live near the beach
 We
went to a fundamentalist Mosque to
find out what Muslims think…
Averages:
 Americans
are better off than ever; the
average salary of an American worker is
now $28,400.
 The
average pollution of air by factories
is now well below the dangerous level.
Beware of “Average”
 Mean:
Add all values and divide by n
 Median:
List all values, low to high,
then take center (half above, half below)
 Mode:
Value that appears most
frequently
Average salary?
 Mean-
very high salaries of few skew
the average, badly. Use if you want to
inflate average salary
 Median
& Mode – not affected
Average Pollution

What happens if only a few factories
are very very horrible polluters, at above
an extremely harmful level?
& Mode – No danger
 Mean? - Very bad, on average.
 Median
 Chrome
Plating shops…
With Averages also Need
Range and Distribution…
Range – gap between smallest and largest
 Distribution – How frequently each value
occurs.
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Ex: Average mercury content in fish is very
low…
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What happens if 10 percent have dangerous
levels?
On average, only 0.2 percent of landmines in
the 25 fields were still active…
Averages, Range and
Distribution….
America is not overcrowded. Nationally,
we have fewer than 60 people per square
mile, a population density lower than that
of most other countries…

Some areas really ARE crowded.
 Some are mostly unpopulated…
When an average is
presented….
 Check
which type of Average you’re
seeing…
 See if the range and distribution might
be important…
Prove One Thing, Conclude
Another….
A car dealer considered a particular car a big
success because only 5 out of 100 buyers who
bought the car had complained to the
dealership about its performance. “When 95
percent of buyers are pleased,” the salesman
says, “then that’s a darn good car…”
• Assumptions?
• All complaints came to dealer
• Non-complainers were pleased
How would you get this
conclusion?
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Conclusion: Car was a high quality success…
Was this supported?
Blind yourself to communicators statistics
How would you actually test this?
Random sample of many of this car’s
buyers and ask them how pleased there
are with the car.
Second Strategy, What Do
Stats Say?
 Look
at Stats alone…
 Only 5 out of 100 buyers who bought
the car had complained to the
dealership about its performance.
 What
can you conclude from this?
95% didn’t have a complaint that required
a dealer visit. Might not like the car, but
not enough to complain…
Example
 Almost
one-fourth of children are
arsonists. Children all over the country
were surveyed. Of the 90 who replied to
the survey, 24 percent said that they
knew of instances in which children set
fires….
 Problem??
Example II
 Women
are better drivers than men, as
proven by the fact that of men involved
in accidents, 23 percent had been
drinking-compared to 9.6% of women…
 Problem?
Deception by Omission…
 Ask
yourself, “What further information
do you need before you can judge the
impact of the statistics?”
Evaluate:
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Fizz aspirin works 50 percent faster
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Than what????
Funding for AIDs research is more than
adequate. Last year the government spent
over 1.2 billion on AIDS research.
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How does this compare
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Over time?
Other diseases?
Total budget?
College degrees pay off. A recent survey
found that workers with a bachelor’s degree
were earning an average of $35,000 per year
in the spring of 2000.
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Where is the comparison of equally intelligent noncollege students? What type of average?
Evaluate:
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A crime wave has
hit our city.
Homicides have
increased by 67
percent in the last
year…
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Problem- What are
the absolute
numbers?
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3 to 5, versus 300
to 500…
Conclusions
Ask – How does the author or speaker
know? What are their motivations?
 How did they choose their sample?
 Be curious about types of averages
 Blind yourself to the stats and see what stats
you would want to support conclusions. Do
they match?
 Look only at Stats and form your own
conclusion. Does it match?
 What information is missing? Take care with
misleading numbers and percentages and for
missing comparisons.
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