1. Introduction to the Logic of
Social Inquiry
Dr. John Bradford

2. Three types of Studies
• There are 3 different types of studies that
correspond to 3 different sorts of dependent
variables (Y), or objects of investigation…
1. Case study (what causes an event or condition)
– Often we aren’t interested in Y itself as a fact or
event, but changes in Y across time (longitudinal study)
or differences in Y across space (cross-sectional study).
2. Cross-sectional study (comparison across space)
3. Longitudinal study (comparison across time)

3. Three types of Studies
Examples:
• Why did people vote? (Case
Study)
• Why does voter turnout
vary from state to state in a
single national election?
(Cross-section)
• Why does voter turnout
vary in the same city year
after year? (Longitudinal)

4. Three types of Studies
We find that voter turnout varies
according to the weather. Let’s say
that the observed turnout is the line
from P (very bad weather) to C (very
good weather). We can explain the
difference between P and C using
longitudinal or cross-sectional
analysis, but we do not explain why
in very bad weather, the turnout is P
(and not Q or R), and why, in very
good weather, the turnout is C
(rather than D or E).

5. Key points about ‘explanations’:
1. Explanations must specify causal
mechanisms, i.e. how something happens.
2. Correlation is not causation
3. Causal explanations can be distinguished from
‘just-so stories’ and ‘as-if’ explanations.
– just because a model can explain something, doesn’t
mean it does. Many hypotheses (models) can
account for the same Y. “Explanation” requires
further proof and refutation of alternative theories.
4. Explanation is not prediction!
– We can explain historical events only after the fact.

6. Three Simple Steps to Social Science
STEP 1: Select some concepts of interest
(variables)
STEP 2: Posit (suggest) some relationship
between these concepts (Hypothesis)
STEP 3: Test these suggestions empirically to
see if they are right.
*STEP 4: Refuting Other Theories

7. Three Simple Steps to Social Science
(More Details)
STEP 1: Select variables
– The dependent variable (Y) is the thing you are
interested in explaining. It is also called the
explanandum.
– Select something to explain, and establish it is factually
correct; -Establish that an event or ‘fact’ (pattern)
exists!
STEP 2: Specify a Hypothesis
– Specify a causal hypothesis (usually from a more
general theory) that explains the phenomenon: if the
hypothesis (X) is true, the explanandum (Y) logically and
necessarily follows.
– If successful, this will show that your explanation is
‘sufficient’: it can account for Y

8. Three Simple Steps to Social Science
(More Details)
STEP 3: Testing your Hypothesis
**Step 4: Refuting other Theories
Assuming your hypothesis seems to explain the dependent variable, what
happens if several other hypotheses seem to explain it equally well?
Basically, you choose the hypothesis (theory) that explains the most
stuff…
1. Identify other possible causes (rival accounts) of the phenomenon.
2. Refute these other theories by showing that other implications (which
necessarily would occur if the hypothesis were true) are in fact not
observed
3. Show how other implications of your theory are in fact observed.
– If successful, this will show that your hypothesis/model is ‘necessary’, it
best accounts for the phenomenon because alternative explanations are
refuted!

9. Three Simple Steps to Social Science
(More Details)
Example: Why are there more
standing ovations at Broadway
plays today than in the past?
Hypothesis: “When people have
paid a great deal of money or
effort to obtain a good, they tend
to value it more highly than when Standing ovation
they paid less for it”
X = ticket prices  Y = standing
ovations

10. Three Simple Steps to Social Science
(More Details)
Support from below:
– What else would be true if our
hypothesis were true?
– {Can we deduce and verify other facts
from the hypothesis different from the
dependent variable (Y)?}
Standing ovation
Example: We should expect fewer
standing ovations in Broadway
plays with cheaper ticket prices.

11. Three Simple Steps to Social Science
(More Details)
Support from above: Can we deduce
the hypothesis from a more general
theory?
Example: The hypothesis above is an
example of the theory of cognitive
dissonance: people will usually find
it easier to persuade themselves Standing ovation
that the play was really good, than
to admit to themselves that they
paid a lot of money to see a bad
show.

12. Three Simple Steps to Social Science
(More Details)
Lateral Support: Can we think of
and refute alternative theories?
One has to play devil’s advocate.
Example: Perhaps shows are just
better today than they used to
be. If this were true, we should Standing ovation
find that they have better
reviews.. Or….

13. Steps in devising and testing an
explanation
• If several hypotheses seem
to explain the same thing
equally well, we pick the
hypothesis (or theory) with
the most ‘explanatory
power’- i.e. that explains
the most stuff.
– This is an ideal
scenario, whereby your
hypothesis, derived from a
theory, is validated, and
alternative hypotheses are
refuted.
– “If this H is true, then
X, Y, and Z must also be true”
• You show that other
implications of your theory
are true (observed), while
other implications of the
other theories are not true
(observed).

14. Common Mistakes in Social Research
1. Contamination
2. Fallacies of presumption
– Hasty Generalization
– False Dichotomy
– Spurious association
– ‘Post hoc’ fallacy
3. Fallacies of the wrong level
– Ecological Fallacy (group to individual)
– Reductionist Fallacy /Fallacy of Composition (individual to
group)
4. ‘Ad Hoc’ Fallacies
5. Misuse of Variance

15. I. Problem of Contamination
• Suppose that there is so much heat given off in the
first test tube, Y₁ that it spreads and heats up Y₂ . This
is contamination!
• The Error of Contamination occurs when the social
researcher acts as if the influence of an independent
variable is restricted solely to experimental group
when in fact it is also influencing the ‘control group’.
Influencing the control Y₂
Y₁

16. I. Problem of Contamination
• One cannot assume that a change in an
independent variable (X) affects the
dependent variable (Y) only in those settings
where the independent (X) variable is present
or has changed.
• Why? Because people observe what happens
elsewhere. The mere existence of some X in
some setting, may affect Y in other settings
where X isn’t present, or has changed.

17. I. Problem of Contamination
Example: Sweden v. Norway
• The effect of Norway’s entrance
into World War II (X) on fertility
rates in Norway (Y₁), using Sweden
(Y₂) as a control.
• An invalid inference might be: “If
Norway had not been invaded in
1940, its fertility rates would have
been like Sweden’s at that time”

18. I. Problem of Contamination
Example: Sweden v. Norway
• One problem (among many) is that
Sweden is not a good ‘control’, even if it is
exactly like Norway in all other
conceivable characteristics, and even if it
was an exact replica of Norway.
• Because Sweden was also affected by the
Nazi invasion…

19. II. Fallacies of Presumption
1. Hasty generalization: making a general
conclusion based on too little information
– My former husband was a jerk…from that I learned
that all men are jerks.
2. False Dichotomy (also called “False
Bifurcation”, “Black and white fallacy;”
“either/or fallacy” “False dilemma.” ): involves
turning a complex issue into one that has only
two choices that are opposite of one another
– ‘You are either with or against us!’

20. II. Fallacies of Presumption
3. Fallacy of false cause (spurious association)
– It says (wrongly) that if two things are
associated, then one of them must be the cause
of the other. If A and B are associated, then A
must cause B.
– Example: More and more young people are
attending high schools and colleges today than
ever before. Yet there is more and more juvenile
delinquency among the young than every before.
This makes it clear that these young people are
being corrupted by their education.

21. II. Fallacies of Presumption
3. Fallacy of false cause (spurious association)
• ‘Post hoc’ fallacy: a more specific form of spurious
association, which asserts that, if A occurs before
B, then A is necessarily the cause of B.
– Derived from the Latin phrase,“Post hoc, ergo propter
hoc” (Latin: After this, therefore because of this).
• Example 1: 98% of Heroin users started off with
marijuana. Therefore, marijuana smoking causes
people to go on to the hard stuff.
• Even more drank alcohol, and 100% drank water!
Only about 1% of marijuana users end up using
heroin.

22. II. Fallacies of Presumption
3. Fallacy of false cause (spurious association)
• ‘Post hoc’ fallacy:
• Example 2: Dr. Manfred Sakel discovered in 1927 that
schizophrenia can be treated by administering overdoses
of insulin, which produced convulsive shocks. Hundreds of
psychiatrists drew a faulty conclusion and began to treat
schizophrenia and other mental disorders by giving
patients electric shocks without insulin. So, they skipped
the insulin but went to shocks. At a psychiatric meeting
some years later, Dr. Sakel sadly came forward to explain
that electric shocks are actually harmful, while insulin
treatment restores the patient’s hormonal balance. The
doctors had confused the side effect with a cause.

23. III. Fallacies of the Wrong Level
• Ecological fallacy: studying something with
the group as the unit of the analysis and
making inferences about the individual
– Group  Individual
• Reductionistic fallacy: studying something
with the individual as the unit of analysis and
making inferences about the group
– Individual  Group

24. III. Fallacies of the Wrong Level
Ecological fallacy: (inferring lower from higher
levels, or parts from wholes)
• Example 1: In the United States presidential
elections of 2000, 2004, and 2008, wealthier
states tended to vote Democratic and poorer
states tended to vote Republican. Yet wealthier
voters tended to vote Republican and poorer
voters tended to vote Democratic.
• The error would be to assume that, because
wealthier states voted Democratic, wealthier
voters also tended to vote Democratic.

25. III. Fallacies of the Wrong Level
Ecological fallacy: (inferring lower from higher
levels, or parts from wholes)
• Example 2: In American cities, there is a strong
relationship between illiteracy rate and
proportion of people who are foreign born. Does
this association hold for individuals? No, it could
be that all the foreign born are highly
literate, they just gravitate to urban areas where
there are also lots of native born people who are
illiterate.

26. III. Fallacies of the Wrong Level
Ecological fallacy: (inferring
lower from higher levels, or
parts from wholes)
Example 3:
• Suppose you flip 10 unbiased
coins 5 times.
• A count of all of the coin tosses
will be pretty close to 25 heads
and 25 tails or 50-50%.

27. III. Fallacies of the Wrong Level
Ecological fallacy: (inferring lower from
higher levels, or parts from wholes)
Example 3:
• Some coins, however, will have more
heads than tails, others will have more
tails than heads, for entirely random
reasons.
• We cannot infer from the overall
distribution of heads and tails (50-
50%), the specific distribution of heads
and tails for each coin!

28. III. Fallacies of the Wrong Level
Reductionist Fallacy (aka Fallacy of composition):
(inferring higher levels from lower levels, or the
whole from the parts):
• Example 1: ‘Paradox of Thrift.’ Saving is good for
an individual, but not necessarily for the
economy as a whole, because lack of spending in
the aggregate can cause a recession.
• The error would be to assume that what
individual interest necessarily coincides with
collective or aggregate welfare.

29. III. Fallacies of the Wrong Level
Reductionist Fallacy (aka Fallacy of composition):
(inferring higher levels from lower levels, or the
whole from the parts):
• Example 2: ‘Dream Team’: Consider the study of
basketball. Suppose you gather together the best
players in the world. Does this mean that your
team will naturally be the best? Not necessarily.
(All these great players might have such great
egos that they can’t manage to play together; a
team of mediocre players might click so well that
they are unbeatable as a team).

30. IV. Non Sequitur
• Non sequitur fallacy (non-SEK-wa-tuur): the
term is Latin for “it does not follow.”
• In logic, the term is used to indicate a
conclusion that can not be justified by the
premises or evidence offered in an argument.
In other words, the non sequitur fallacy occurs
when an the conclusion does not follow from
the premises.

31. IV. Non Sequitur
Argument A:
(1) Most poor people don’t commit crimes
(2) Some rich people commit crimes
• Therefore, there is no relation between poverty
and crime!
Argument B:
1. Most people with bullet wounds don’t die.
2. Some people without bullet wounds do die.
• Therefore, bullet wounds are not a direct cause
of death. ?????

32. V. Misuse of variance
• Most quantitative methods in the social
sciences (e.g. statistical regressions) explain
the differences or variation in a dependent
variable (Y), not the existence of the
phenomenon itself.
• This approach is fine for many
purposes, but it cannot be used to study or
to identify fundamental causes, (i.e.
constant forces).

33. V. Misuse of variance
Gravity: A Lesson for Social Research
• If you drop a feather and a brick from the
same height they will, in most empirical
circumstances, reach the ground at
different times.
• A typical social scientist will explain by
attempting to account for the difference
between the velocity of the brick and the
velocity of the feather.
• Y = difference in velocity, NOT velocity.

34. V. Misuse of variance
Gravity: A Lesson for Social Research
• The social scientist may then figure out
that air resistance is an important factor
explaining much of the variance. He or
she may then run many regressions
testing a number of possible factors, to
ferret out the ‘net effects’ of all of the
independent variables.
• Once the variation is
‘explained’, however, do we have a
complete explanation of the phenomenon
of falling bodies? What’s missing from
this picture?

35. V. Misuse of variance
Gravity: A Lesson for Social Research
– Answer: the social scientist would never
have discovered gravity! Certainly any
adequate account of falling bodies must
also explain not only the differences in
their rate of fall, but more
importantly, why they fall in the first place!
– Likewise, social scientists who are only
concerned with explaining away variation
(‘variance’ or differences), will miss entirely
the fundamental causes or driving forces
behind these phenomena.
– To examine only the differences between
variables ignores their similarities!