Causal Reasoning
Inductive because it is limited by our inability to
know (1) all of the relevant causes, and (2) the
ways in which these causes interact
We can address uncertainty by speaking not of
CAUSES, but of CAUSAL FACTORS
Main danger to avoid is the Post Hoc fallacy:
inferring that X caused Y because it happened
prior to Y. This creates a False Cause.
Mill‟s Methods for Analyzing
Causes
Method of Agreement: look for common factor in
all cases where the effect is present
Method of Difference: look for factor that is
present when the effect occurs, and absent
when the effect does not occur
Joint Method: combination of Agreement and
Difference
Method of Concomitant Variation: used when
effect comes in degrees; look for a factor that
varies along with effect (correlation)
Correlation
A correlation is a (statistical) measurement of
the association of two variables.
Positive Correlation: As one variable increases,
the other increases. (Examples: cigarette
smoking and lung cancer; education and
income; unemployment and homelessness)
Negative Correlation: As one variable increases,
the other decreases. (Examples: caffeine intake
and sleep; age and working memory capacity;
stress and life expectancy)
Identifying and Assessing
Correlations
Correlations are identified by: r=.
Correlations range between -1 and 1; positive numbers
identify positive correlation, negative numbers identify
negative correlation. r=0 is no correlation.
The further away from 0 the correlation is, the more
strongly the variables are related. Correlations above .5
or below -.5 are strong correlations; correlations between
.2 and .5 (or -.2 and -.5) are moderate correlations.
r2 will give us the percentage of difference in one
variable that is due to difference in the other. (Example:
if the correlation between smoking and lung cancer is .7,
49% of differences in lung cancer rates are due to
differences in smoking levels.)
2 Basic Forms of Statistical
Reasoning
Statistical Syllogism: x% of A is B; p is an A;
therefore p is a B (to x% likelihood). (Example:
86% of college students are broke. Fred is a
college student, so it‟s pretty likely that he‟s
broke.)
Inductive Generalization: x% of known As are
Bs; therefore x% of As are Bs. (Example:
Almost all of the students in this logic class
hated the Deductive Reasoning assignment.
Thus, I should expect that almost all students in
any logic class would hate that assignment.)
Components of a Statistical Study
Target Population: This is the group about which you
want to make an overall judgment. It could be all people,
voters, college students, etc.
Sample (or Experimental) Group: This is the group
studied or experimented upon to get information used to
infer claims about the Target Population.
Control Group: Needed whenever one is looking for
differences between groups; this group serves as an
“anchor” against which to evaluate the Experimental
Group. The Control Group helps to weed out spurious
results. (Example: If you want to see if viewing
pornography alters perceptions about women, you need
a Control Group that takes the same questionnaire but
does not view pornography beforehand.)
Sample Size
Indicated by: N=. (Also sometimes ss=.)
Good statistical studies should tell you both (1)
how many subjects one has overall, and (2) how
many subjects are in each group.
Sample size gives us information about how well
results can be generalized from the Sample
Group to the Target Group. The larger, the
better.
This is because in large samples, extreme and
otherwise unrepresentative cases are more
likely to be balanced off.
Hasty Generalization
Small or atypical sample sizes lead to the
fallacy of Hasty Generalization.
The Hasty Generalization involves
inferring claims about the Target Group
from the Sample Group that lack sufficient
support.
Sample Diversity
Sample Diversity is important because it (1)
helps to balance off extreme or unrepresentative
cases, and (2) reduces the likelihood that the
study reflects the researcher‟s biases.
Representative Sample: sampling picked to
match, as closely as possible, the actual
distribution of traits in the Target Population.
Random Sample: sampling based on some
arbitrary and irrelevant criterion.
Other Guidelines for Evaluating
Statistical and Demographic Data
Date of Study: While older studies can still have cogent
results, in many cases new research (and new
methodologies) may have invalidated the previous
results.
Author and Sponsor of Study: Is the study being
produced by (or funded by) someone with a stake in how
the results turn out? This can increase the likelihood
that biased research methods were used.
Publication Conditions: Studies published in peer
reviewed journals have their findings analyzed by other
experts in the field, some of whom disagree with the
author. Beware of studies that are neither peer reviewed
or reviewed only within an organization.
Statistical Significance
Indicated by: p= (); this is a
measurement of how likely it is that the
results of the experiment are due to
chance factors.
This is NOT „significant‟ in the sense of
„large‟, NOR in the sense of „important‟.
Researchers usually declare a finding
statistically significant if p < .05.
Statistical Significance Continued
Failing to attain a statistically significant result
should not necessarily be viewed as a failure.
The finding that two groups do NOT differ in a
reliable way (affirming the Null Hypothesis) can
be a highly important finding.
Statistical Significance is linked to the
importance of replication in scientific
experimentation. A study with p=.05 is still 5%
likely to have its results due to chance. Think of
Significance as a claim on the likelihood that
repetition will produce the same results, and
replication as a test of this contention.
Margin of Error
Margin of Error: this is a measurement of
variability in the sample. A standard
margin of error for well-conducted surveys
and polls is +/- 2 to 3%. This will give us
the range of the study. (Example: if a
study shows that 51% of IVCC students
prefer Coke to Pepsi, with a margin of
error of 3%, this means that between 48-
54% of IVCC students prefer Coke to
Pepsi.)
Base-Rate Data
Base-Rate Data is information that tells you how
prevalent some trait is within the general
population, or how likely the occurrence of some
event is independently of what we do.
This is crucial when you are checking for causal
factors for ruling out spurious causes.
Example #1: Freud‟s “It Works!” Argument
Example #2: John Hinckley‟s brain
Example #3: Post-9/11 airport security
Analogies
Analogies are prevalent in literature, philosophy,
religion and law
In literature and religion, they are often present
as comparisons, metaphors and parables.
In law, they are typically present as precedents
and hypothetical cases
In philosophy, they are typically present as
thought experiments (“intuition pumps”)
Analogies are even present in science—esp. in
scientific discovery and in science education
Steps for Analyzing an Analogy
(Simplified)
Clarify the terms of comparison
Identify the principle or characteristic that
is being applied
Identify relevant similarities (False
analogies rely on trivial similarities.)
Identify relevant differences
Weigh up relative strength of similarities
and differences to reach a final
assessment of strength
Example
Iraq is the new Vietnam. In both cases, our enemy is
some nebulous, indefinable entity (communism,
terrorism). In both cases we lost many American lives
from insurgency for which we were unprepared. Both
wars seem like futile endeavors with no hope for
success. In each case, we lacked support for the war,
both at home and abroad. Presidents Johnson and
Nixon both escalated the war in Vietnam in response to
popular dissent; President Bush has responded to
popular dissent by sending more troops. Mission creep
in Vietnam led us to invade Cambodia; the Bush
administration has been talking about expanding the Iraq
war into Iran or Jordan. History‟s verdict on the Vietnam
War is clear: it was an unjustifiable act of aggression.
Shouldn‟t we view the Iraq war in the same way?