1
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
19
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
22
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