Logic of social inquiry

Logic of Social Inquiry

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)

Three types of StudiesExamples:

• 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)

Three types of StudiesWe 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).

Key points about ‘explanations’:

1. Explanations must specify causal mechanisms, i.e. how something happens.

2. Correlation is not causation3. 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.

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

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


STEP 3: Testing your HypothesisSTEP 4: Refute Other Theories1. 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!


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 they paid less for it”

X = ticket prices;

Y = standing ovations

Standing ovation


Support from below: Can we deduce and verify other facts from the hypothesis different from the dependent variable (Y)?

Example: We should expect fewer standing ovations in Broadway plays with cheaper ticket prices.

Standing ovation


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 that the play was really good, than to admit to themselves that they paid a lot of money to see a bad show.

Standing ovation


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 find that they have better reviews.. Or….

Standing ovation

Steps in devising and testing an explanation

• 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”

• Show that these other implications are true for your theory, and not true for competing theories.

Common Mistakes in Social Research

1. Contamination2. 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’ Fallacies5. Misuse of Variance

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’.

Y₁ Y₂ Influencing the control


• 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.


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”


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…

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!’


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.


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.


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.

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

• Reductionistic fallacy: studying something with the individual as the unit of analysis and making inferences about the group


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.



• 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.



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%.



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!


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.


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).

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.

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. ?????

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).

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.

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?

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!

Logic of social inquiry

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