Statistics
Statistics is simply a mathematical science that gathers
information about a population so that population may
be described usefully. Statistics are often used to draw
conclusions and make decisions based on that infor-
mation. So, what’s the problem?
Statistics are complicated and their problems can
be numerous. In general, though, problems with sta-
tistics are similar to those of other types of numerical
data; namely, they can be gathered, analyzed, and/or
interpreted incorrectly, or mishandled by someone with
a bias. Let’s look at two common problems with sta-
tistics. The first question to ask is, is the statistic mean-
ingful? Many parents worry, for instance, when they
hear that the average baby walks at 13 months. They
conclude that there must be something wrong with
their 18-month-old who is still crawling. But, it has
been proven that babies who walk later have no devel-
opmental differences at age two from their early-walk-
ing peers. In other words, the statistic is not meaningful;
there is nothing wrong with an 18-month-old who is
still crawling.
Another example: when standardized test scores
were analyzed across the country, it was concluded that
students from wealthy communities were smarter than
students in poorer communities because their scores
were higher. Is this a meaningful, accurate conclusion?
Probably not. It does not take into account the many
other variables that can account for lower test scores,
such as inferior preparation, fatigue, and even break-
fast on the day of testing.
Practice
Evidence shows that most car accidents occur on days
with clear weather than on days when it is snowing. Can
you conclude that it is safer to drive when it is snow-
ing? Why, or why not?
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Answer
No, the conclusion that it is safer to drive in the snow
is wrong. There are other factors influencing this sta-
tistic, such as there are more clear days than snowy days,
and more people are probably on the road in clear
weather than snowy weather.
A second question to ask: is the statistic given in
such a way that it misrepresents the data collected?
Does it make the data sound better or worse than it is?
Suppose a survey was done to see how many children
live below the poverty line. We hear it reported on the
news: “80% of all children live above the poverty line.”
What about the 20% who live below it? The declaration
of the 80% sounds good, while shifting the focus away
from the millions of children who are poor. What
about: “Women earn an average of 70 cents for every
dollar earned by a man.”This sounds unfair, but it does
not tell you which jobs are being compared, how long
men and women have worked at those jobs, and
whether men work longer hours because they do not
take as much responsibility for child care.
–MISUSING INFORMATION—THE NUMBERS GAME–
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Practice
Researchers found that 98% of juvenile offenders com-
mitting serious crimes watch violent TV shows on a
regular basis. If you are an advocate for a reduction in
TV violence, how would you use this statistic? What if
you were an advocate for freedom of expression on tel-
evision?
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Answer
As an advocate for a reduction in TV violence, you
would probably say, “watching violence on TV turns
our young people into criminals.”If you were an advo-
cate for freedom of expression on television, you might
find out the real number of young people in the 2%.
Let’s say it is 3 million. You might conclude that “mil-
lions of children watch violent programs regularly, and
they don’t end up as criminals.”
Another common way in which statistics are
manipulated is by leaving out key information. For
instance, a company claims it is edging out its com-
petitor with higher sales. They are correct in stating that
they have had a 50% increase in sales, compared with
only a 25% increase for their competitors. Is their claim
valid? You can’t know unless you have more informa-
tion. What if the competitor sold two thousand bicy-
cles last year, and 2,400 this year; the other company
sold 40 bicycles last year, and 60 this year. Edging out
the competition? Hardly.
When you hear a statistic, either in an advertise-
ment, a political speech, a newspaper article, or other
source, remember that it is not necessarily true. Then,
ask yourself three questions: Is the statistic meaning-
ful? Does it deliberately misrepresent the data collected?
Does it give you all the information you need to eval-
uate it? Thinking critically about statistics will help you
to avoid making the wrong conclusions, or relying on
information that is faulty or simply untrue.
Practice
What is wrong with the following statement?
Russians are better off than ever; their
average worker’s annual salary is now
$20,000.
Answer
Compared with what? This statistic is meaningless as
it is stated because it leaves out too much information.
There is a big difference between the salaries of the
wealthy business class and the workers. Inflation is also
a factor. If $20,000 is worth less now than it was five
years ago, the average worker could be doing worse than
ever.
In Short
It is just as easy to deceive with numbers as it is with
words. Surveys, studies, and statistics are conducted and
interpreted by researchers who might have a bias, or
simply lack the skills necessary to do their jobs prop-
erly. Therefore, it is important to evaluate numbers
before accepting them as truth. Ask questions about
how the information was gathered, what its margin of
error is, and how meaningful it is. Does the conclusion
make sense, or does it seem to distort the findings?
Thinking critically about the many numbers you
encounter will help you to rely only on information
that is objective and accurate.
–MISUSING INFORMATION—THE NUMBERS GAME–
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–MISUSING INFORMATION—THE NUMBERS GAME–
85
Skill Building Until Next Time
■Watch a news broadcast and listen for the results of a survey or poll. Does the newscaster tell
the margin of error? Why is it important to know this number?
■Look for a print advertisement that includes a statistic. Why was it included? Does it seem accu-
rate and objective? How else could the advertiser have made the point without using numbers?
ITISAwidely held belief that emotions are an enemy of critical thinking. The theory goes that the
head is rational, while the heart is emotional, and any objective thinking or decision making should
be done with the head. In fact, the word objective means “not influenced by emotions or prejudices.”
But can you, and more importantly, should you, completely ignore your feelings when engaged in critical
thinking?
Surprisingly, the answer is no. Emotions or feelings have a place in critical thinking, just as logic and
reason do. But they must be recognized and used judiciously. That is to say, your decisions should not be
reached quickly, solely on the basis of your feelings, and there are some emotions that are best recognized
and then left out of the process. The goal in critical thinking is to acknowledge and understand the emo-
tions that may influence your decision making, so you can determine when and where to let them become
part of the decision-making process. If you can accomplish this, you use or listen to your emotions in a rea-
sonable and rational way. They are not in control of you, but rather you are in control of them.
LESSON
Checking Your
Emotions
LESSON SUMMARY
In this lesson, you will discover the role that emotions play in the deci-
sion-making process. When emotional responses are recognized and
used appropriately they can be an effective piece of critical thinking.
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