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Quantitative Reasoning

Spring 2011 Lecture Notes

www.ilstu.edu/~oaajayi

2Week 3 Assignments

Start work on choosing a topic – due 2/2

Start literature review

Use Library links

Bring to class any questions

3Week 3: Why are we here?

To understand how research is conducted

Better understanding of research results

Improved ability to conduct original research

Tools to evaluate research

Interested in scientific research

That which satisfies certain criteria

What are these? First we must define some terms:

4Definition of science

“An attempt to identify and test empiricalgeneralizations”

Empirical Facts

The “real world”

That which exists and can be known through the experiences of our senses

Normative Judgments about what should be

5Science – testing and generalization

Attempts to test empirical statements

Testing must be

Objective (Intersubjective testability)

Results must be independent of researcher bias

Findings only accepted if they can be replicated

Generalization of results

Results must extend to the general from the specific

Example:

Mr. Williams, college student, does not vote

Ms. Young, State Farm worker, always votes

What does this tell us?

Nothing

A specific experiment, with a large enough sample, may find

that workers vote, students do not

6Science

Attempts to explain and predict

Requires generalization

Logic:

Generalization: high ethnic conflict, coup d’etat

Observation: high ethnic conflict in 1985

Explanation/Prediction: coup d’etat

Generalizations are almost never absolute

So why bother?

Usually probabilistic … X is more likely if Y

7Normative versus Empirical

Empirical statements

Refer to what is true or false

Can be confirmed or disproved by sense

experience

Objective analysis of data from sensory observations

May be questions or statements

May deal with past, present, or future

8Normative statements Deal with what is

Good or bad

Desirable or undesirable

Beautiful or ugly

Cannot be answered objectively Depend on value judgment

Even if all agree with the statement, may still be normative – i.e. not empirically testable E.g. Murder is bad

9Analytical statements

Validity is dependent on assumptions or definitions, not empirical observations

Example

Is it possible for a candidate to be elected president by the electoral college without having the greater number of popular votes?

10Normative to empirical Normative questions are often the most interesting

to answer Science cannot answer such questions … or can it?

To answer normative questions, scientific research must reformulate them as empirical questions by Changing the frame of reference

Ask empirical questions about the assumptions behind normative statements

11Changing the frame of reference

Example

Normative statement

Should smoking be banned in all public places?

Changed frame

Do most college students favor a public places smoking

ban?

Limitations

May produce “trivial” results for some topics

12Empirical question about assumption

Example

Normative statement

Should smoking be banned in all public places?

Empirical question about assumption

Would banning smoking in public places result in fewer deaths

from smoking-related illnesses?

Limitations

Can never actually answer a normative question

Can ALL assumptions behind a normative question be

identified and tested?

Even if yes, person may still hold their normative position

13Week 3 Review

Why are we here?

To identify and test empirical generalizations

What is a normative statement?

What is an empirical statement?

What are 2 ways a normative statement can

be changed to an empirical statement?

Change frame of reference

Ask empirical question about assumptions

14Week 3 Review

Normative statement

Coke is better than Pepsi

Frame of reference method

80% of ISU undergrads think Coke is better than

Pepsi

Empirical assumptions method

Coke has less sugar than Pepsi

Coke has fewer calories than Pepsi

1515Exercises

If a foreign policy decision would increase

U.S. exports, then that’s what should be done

Normative or Empirical?

Normative

Why?

“should”

Convert to empirical using frame of reference

method

75% of the American public believe that if a

foreign policy decision would increase U.S.

exports, then that’s what should be done

1616Exercises

If a foreign policy decision would increase

U.S. exports, then that’s what should be done

Convert to empirical using empirical

assumptions method

Why would someone think increase US exports is

a good thing?

Would result in increased GDP

Empirical statement: Foreign policy decisions that

increase US exports result in at least a 5%

increase in GDP

17Exercises Allowing people to carry concealed weapons

lowers the crime rate Normative or Empirical

Empirical

Why? Can be proven or disproven based on facts

People who think that politicians are dishonest are less likely to vote than those who trust government Normative or Empirical

Empirical

Why? Can survey citizens on honesty of politicians and likelihood of

voting

1818Exercises

Negative campaign advertizing is what’s wrong with elections today

Normative or Empirical Normative

Why? States an opinion

Convert to empirical using empirical assumptions method

Do more non-voters report dislike of negative campaigning as at least one reason for not voting in the 1990s as compared to the 1970s?

Topic Paper Advice

Don’t worry about an empirical statement at

this point

Don’t worry about the position you will take

on the topic at this point

Report ALL positions

Keep an open mind, go and see what the

literature says about your topic

Report those findings faithfully

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20Topic Paper Example

Household pets

My family has often debated the best choice of

household pet. The younger and less responsible

family members argue for fish as they require the

least effort. Similar arguments are made for

turtles. Others in the family say cats make the

best pets since they are clean and can be left

alone and trusted not to destroy the house.

Personally, I vote for dogs since they are loyal

and can provide protection. I hope that in this

paper I will be able to prove that one type of pet is

best to keep in a home.

21Topic Paper Example

(Light Literature Review)The literature on household pets is varied. Some authors hold that pets requiring minimal effort to maintain are the best choices for families. These pets range from tortoises to fish to cats. Dr. A, for example, argues that minimal effort increases the likelihood of the pet living a long and enjoyable life while at the same time providing companionship to its owners.

The quality of interaction between pet and owner is the focus of another set of authors. Here it is argued that the best kind of pet is one that matches the energy level of the owner. As an example, Dr. B states ….

Note that the position is stated and supported by quotes from articles

Topic Paper Example

What are you going to need?

NUMBERS from those who hold each position

Survey of pet owners who give reasons for choosing a

pet

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23Paper Overview

Section % Points

Topic – Due 2/2 10 95

Lit Review

Research Question

15

10

142.5

95

Hypothesis

Variables

Research Design

10

15

10

95

142.5

95

Data 15 142.5

Conclusions 15 142.5

Total 100 950

24Full Literature Review

Use Library sources for identifying positions

Rely only on scholarly works

Journals

Articles

Books

Use internet sources sparingly

Remember give POSITIONS supported by

articles

25Developing Research Questions

Once literature review complete, should have

ONE position you wish to test

From that position, develop an empirical

statement

Need to develop a research question

Must satisfy certain criteria

26Research questions

Criteria

Clarity

Testability

Theoretical significance

Practical relevance

Originality

27Clarity

Specific enough to direct research

General enough to suggest a possible answer

Bad example

Why don’t Americans vote?

Improvement

Is voter turnout reduced by political alienation?

Does election day voter registration increase turnout?

Do not limit to particular locale

Reduces theoretical significance and practical relevance

May have to as a matter of practicality

In such cases (actually, in all cases), design question so as

to be repeatable in other locales

28Testability

An absolute requirement

Must be an empirical question

Can the investigation be carried out with

available resources?

29Theoretical significance

Answer to the RQ should increase general

knowledge & understanding of the topic

Requires a thorough literature review

What past research findings exist?

What do others generally assume to be true?

Should build on previous research

Major motivation is suspicion that existing

explanations are flawed or no longer applicable

30Practical relevance

Answers should be useful

Provide help in accomplishing some goal

Example

Have time limits on eligibility for welfare payments

increased employment rates among past recipients?

31Originality

It is often not useful to rehash studies that

have been conclusively answered

Such studies should only be conducted if some

additional theoretical significance will be

uncovered

32Review

What is a normative statement?

What is an empirical statement?

What are 2 ways a normative statement can

be changed to an empirical statement?

Change frame of reference

Ask empirical question about assumptions

What are the five criteria for Research

Questions?

Clarity, Testability, Theoretical significance,

Practical relevance, Originality

33Review, Continued

Statement

McCain was right to select Palin as his VP

Normative because “right” implies a value statement

Made empirical: Frame of reference method

85% of the American public believe Palin was the

right choice

Made empirical: Empirical assumptions

method

Selecting Palin will result in more social

conservatives and women voting for the

Republican ticket

34Week 4 Assignments

Complete and submit topic paper

Start full literature review

Think about potential research questions