Chapter 4
Inductive Arguments
Statistical and Causal Generalizations
Intro to Critical Reasoning
Professor Douglas Olena
Fall 2003
This chapter
• The use of statistical evidence in
arguments
• The reporting of statistical data
• The use of causal generalizations
Inductive Reasoning
•
Inductive arguments aim at establishing strong, if not
absolutely certain, conclusions. Inductive strength is
based on good evidence from which we can draw useful
generalizations.
•
Ideally, all of the issues that we face could be resolved
with certainty by following correct reasoning.
•
In our human state, however, very few conclusions can
be proven beyond a shadow of a doubt. 98
Inductive Reasoning
• [T]he evidence does offer strong support for the
conclusion with the reservation that there may
be an unusual exception.
• When we offer evidence that gives weight (but
not complete certainty) to a conclusion, we are
reasoning inductively.
• We speak of deductive certainty, which occurs in
a sound argument, and of inductive strength. 98
Inductive Reasoning
•
If we can present evidence to prove that a premise is very likely to
be true, we have valuable information on which to base our
decisions.
•
Stated in formal terms, “If I encounter A, it is probably a B.
However, I realize that there are exceptions.” 98
•
•
READ illustrations bottom of 98 top of 99.
Critical thinkers use the process of induction to draw reasonable
conclusions and to make thoughtful decisions. 99
Inductive Reasoning
•
Most of the issues we face daily involve inductive
reasoning.
•
We gather facts from our background experiences and
our reading and research—experiential and empirical
data—to come to conclusions that make sense to us
because of their strength. 99
•
•
Breast Cancer illustration middle 99.
When you reason inductively, you look at evidence and
draw conclusions that are not certain, but likely. 100
Inductive Reasoning
• Some scholars believe that many deductive
premises are derived from previous
inductive arguments.
• If you charge more on your credit card than
you can afford, you will get yourself into debt.
100,101
Inductive Reasoning
• In Chapter 4 and 5, we will focus on
methods of examining and assessing the
strength of evidence used to support
conclusions in inductive arguments…. 101
Statistical Evidence
•
Why do we do research aimed at generating accurate
statistics?
•
One motivation for doing research is to have a sense of
control over our individual and collective futures.
•
As critically thinking people, we want to act clearly,
deliberately and responsibly.
•
We want to be prepared for future events. 102
Statistical Evidence
•
As individuals, we reason inductively by generalizing from
observations we make about our own circumstances and
experiences.
•
As a society, we use more formal research methods to get
accurate information about social issues such as rates of disease,
drug and alcohol usage, likely election results and public opinion
about government policy.
•
Statistical research helps us decide which programs should be
funded or denied funding, which should be modified and what
goals we wish to achieve. 102
The Use of Statistics
•
Numerous professions in our culture use statistics.
•
•
•
•
•
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Lending companies
Real estate agents
Weather forecasters
Seismologists
Political advisers
Advertisers
•
Neilsen Ratings give commercial advertisers a good
idea of what television channels are being watched
…. 102, 103
Exercises page 105
• SEXUAL DISEASES ARE A
GROWING SCOURGE IN THE U.S.
• Hidden Epidemic Costs $10 Billion a Year,
Excluding Tab for AIDS.
How Research is Done
•
What do I want to find out?
•
•
Whom do I want to know about?
•
•
This is called the Characteristic of Interest.
This is called the Target Population.
Whom can I study to get accurate answers about my
entire target population?
•
•
•
This is called the Sample.
We study representative members of the population.
For polling, the minimum sample size is usually 1,000.
105
Sample Size
• The Sample must be large enough.
• Any sample studied must be sufficiently
large to justify the generalizations drawn
from the research.
• Otherwise, we are dealing in poor
experimental design or even
stereotyping. 106
Sample Size
•
The Sample must be large enough.
•
Example page 106: “Men are terrible cooks— both my
brother and my boyfriend have burned dinners this
year.”
•
•
•
•
Characteristic of interest: Whether men can cook well
Target Population: One-half~ of the human race
Sample: My brother and my boyfriend
Small studies are less reliable than large studies. 106
Exercise page 107
• State the:
• Target Population
• Characteristic of Interest
• Sample
Sample Size
•
Most of us enjoy giving out opinions but we’re not willing
to find the data that are required to prove our opinions.
•
We get defensive about our pet stereotypes and
indefensible positions and don’t like people to shake us
up.
•
As we become critical thinkers, our positions will be taken
more carefully and backed up with the kind of evidence
that gives us real confidence about the opinions we share
with others. 107
Sample Quality
• For a sample to be representative, it must
have the the same significant
characteristics in the same proportions as
the target group.
• If the sample does not have these
characteristics, then it is called biased.
• A biased sample does not provide adequate
evidence to support a conclusion. 108
Sample Quality
•
Sample randomness is closely linked to the
representativeness of a sample.
•
You can draw solid conclusions about a large target
population by using a much smaller, but representative
and randomly selected, segment of that population.
•
Randomness means that every member of the target
population has an equal chance of being chosen as part of
the sample.
•
A truly random sample is generally representative of the
target population. 108
Questions to Ask
• Analyze the quality of statistical evidence
by noting the size, representation and
randomness of the sample.
• Review the questions page 109, 110.
Surveys as Evidence
• Surveys can be used as evidence, but
particular attention must be paid to the
sample used to generate the statistics.
• The sample must be randomly selected
from a representative group of the target
population. 111
Statistical Generalizations
• Statistical evidence reflects only what can
generally be expected; conclusions about
such evidence are called statistical
generalizations.
• They add strength, not certainty, to your
conclusions. 112
Statistical Generalizations
• Still we need to allow room for the
complexities of individual people and not
expect that what is generally true will be
true for everyone. 112
Exercise pg.112, 113
• At A Lecture—Only 12 Percent Listen
Reporting of Statistical
Studies
• Studies are not usually reported in popular
media in their complete context.
• Distortions occur on that account.
• Attention must be paid both to raw
numbers and percentages. 113, 114
Exercise pg.114, 115
• Family Members, Not Strangers Abduct
Most Children
• Questions 115
Causal Generalizations
•
We attempt to determine causal connections for several
reasons:
•
We seek to eliminate current difficulties and prevent future
problems that arise for individuals.
•
We want to resolve general problems that affect large
groups of people.
•
Much great investigation is motivated by sheer human
curiosity.
Causal Generalizations
• We look for causes of societal problems in
our efforts to ensure that these problems do
not occur again.
• We seek causes to eliminate potential
problems: seat belts, baby furniture and toy
safety, inflationary trends, etc. 115, 116
Hume’s Conditions for
Cause and Effect
1. X, the cause, preceded Y, the effect, in time.
2. X and Y are contiguous (in contact with one
another) in time and place.
3. There is a history of 1 and 2; that is, there is a
history of X preceding Y and of X and Y
being related in time and place. 116
Causal Generalizations
• Even when all of Hume’s conditions are met,
it is hard to distinguish between a correlation
and a specific causation. 117
• Friday the 13th and accidents of a certain
sort. They may be correlated but not caused
by the day/date relationship. The
intermediate factor may be superstition.
Technical Causation
• A necessary condition must be present if the
effect is present.
• Equivalently, if the necessary condition is
absent, then the effect cannot occur. 118
Technical Causation
• Example:
• Oxygen, fuel, heating fuel to the
combustion point
• If there is oxygen and fuel heated to the
combustion point then there will be fire.
• Cyanide, swallowing cyanide.
• If John swallows cyanide, then John will
die.
Technical Causation
• A sufficient condition is a condition that
automatically leads to the production of
another event.
• If the condition is present, then the effect will
definitely occur.
• The sufficient condition creates the effect. It
is the cause of an event. 118
Technical Causation
• Multiple Causes
• A man may die because of multiple causes.
ex. he may genetically have a weak heart.
• He may have a bad diet.
• He may occasionally overexert himself.
• Together these causes may be a sufficient
condition for heart failure.
Technical Causation
• With respect to multiple causation, it may be
difficult to assign correct weight to the causes
beyond a reasonable doubt.
• See the movie “A Civil Action” with John
Travolta 119.
Technical Causation
•
Immediate causes:
•
•
Consider the immediate or situational cause of a problem.
•
Driving Drunk after a party. If alcohol had not been
served, the driver most likely would not have been drunk.
The accident would not have happened. 124
What factor makes the difference between the problem
happening or not happening.
Mill’s Analysis
• Method of Agreement:
• See Chart page 125
• Method of Difference:
• See Chart page 126
Mill’s Analysis
• These methods are used together and
separately to conduct valid research
experiments. 126
• These methods are very useful for analyzing
problems with computers.
Mill’s Analysis
• These methods are used together and
separately to conduct valid research
experiments. 126, 127
• Allergic reaction study, behavior of animals
• These methods are very useful for analyzing
problems with computers.
Review
• Chapter Highlights 128
• Chapter Checkup 128
• Articles for Discussion 129