How Math Can Help You
Choose the Right College
Dr. Geoff Turner
What Today’s Talk WON’T Do
Sadly, I can’t tell you what your ideal
college is.
Nor can I provide an algorithm for finding
your ideal college. (But then again, no one
can.)
Not how psychologists typically use math.
What Today’s Talk Will (Hopefully) Do
• Let you know how psychologists make decisions
and think about how people make decisions (using
math)
• Suggest ideas to help you in your search for a
college
• Available on the web
– web.simmons.edu/~turnerg/choice/choice.ppt
Math in Psychology
Statistical significance:
A difference is not always a difference!
Math in Psychology
Statistical significance:
A difference is not always a difference!
Significant Differences
Significant Differences
22.00
20.00
18.00
16.00
15.46
14.00
15.46
14.01
14.01
12.00
10.00
0
1
2
3
4
Significant Differences
Significant Differences
22.00
20.00
18.00
16.00
15.46
14.00
15.46
14.01
14.01
12.00
10.00
0
1
2
3
4
Detecting Deception
Do “lie detectors” really work?
Polygraph Test
It works!
Polygraph Test
Oops!
How Psychologists Judge Differences
The Mathematical Models
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F = P(“old”|New)= F(- Co )
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RF =P(“remember”|New) = F(- Co )Fç
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Choices, Choices
1. People don’t like choosing (deciding)
2. People have surprisingly little insight
into their own thought processes.
3. People’s choices are remarkably
inconsistent over time, even under
apparently identical conditions.
4. Frequently, our choices are not optimal.
They’re irrational.
What’s for dinner?
If offered the choice between beef and
chicken, you might choose beef.
Beef
≻
Chicken
What’s for dinner?
If offered the choice between chicken and
fish, you might choose chicken.
Chicken
≻
Fish
What’s for dinner?
If offered the choice between fish and beef,
then, of course you would choose …
Beef  Fish ?
Fish  Beef ?
What’s for dinner?
How is this possible?
• Beef ≻ Chicken
• Chicken ≻ Fish
• Fish ≻ Beef
Problem with Decision Models
Intransitivity
(the paper, rock, scissors problem)
The transitive property
If a > b, and b > c, then a > c
but…
Back to Dinner
1 decision, but 2 dimensions
• Beef ≻ Chicken
(Taste)
• Chicken ≻ Fish
(Taste)
• Fish ≻ Beef
(Health)
Two Dimensions
25
Beef
Taste
20
Chicken
15
10
5
Fish
0
0
5
10
15
Health
Transitivity Within Dimension
20
25
Same Potential Issue With College Choice
• Simmons ≻ BU
• BU ≻ Northeastern
• Northeastern ≻ Simmons
Most Real-World Decisions
Are Like This
What Can We Do?
(besides flip a coin)
Multi-Dimensional Scaling
Discover relationships from comparisons:
LA-NY > LA-Denver
LA-Atlanta > Seattle-SF
Multi-Dimensional Scaling
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Repertory Grid (Kelly, 1955)
• Gather a set of schools you think you might be
interested in
• Enumerate all possible triples
# Schools
3
4
5
6
# Triples
1
3
6
10
Next
• Split each triple based on “feel” or intuition whatever comes naturally.
• Define the way members of the pair are similar
(and why they make a pair) and how the third is
different.
• Example: BU, Simmons, Northeastern
BU, NEU vs Simmons
Large vs. Small
Repertory Grid (Kelly, 1955)
Construct a matrix of comparisons:
BU
Wheelock
Simmons
Harvard
NEU
Size: Large
vs Small
1
Co-ed vs.
women
0
0
1
0
0
Focus:
Research vs
Teaching
1
0
0
1
1
Faculty:
Brilliant vs
Ordinary
0
0
1
1
0
Good food
vs. bad
0
0
1
1
1
0
1
Repertory Grid (Kelly, 1955)
Construct a matrix of comparisons:
BU
Wheelock
Simmons
Harvard
NEU
Size: Large
vs Small
1
0
0
1
1
Co-ed vs.
women
0
0
1
0
0
Focus:
Research vs
Teaching
1
0
0
1
1
Faculty:
Brilliant vs
Ordinary
0
0
1
1
0
Good food
vs. bad
0
0
1
1
1
Repertory Grid (Kelly, 1955)
• Sort the Matrix by Element (School) putting similar together
BU
NEU
Harvard
Wheelock
Simmons
Size: Large
vs Small
1
1
1
0
0
Co-ed vs.
women
0
0
0
0
1
Focus:
Research vs
Teaching
1
1
1
0
0
Faculty:
Brilliant vs
Ordinary
0
0
1
0
1
Good food
vs. bad
0
1
1
0
1
Repertory Grid (Kelly, 1955)
• Sort the Matrix by Construct (Attribute) putting similar together
BU
NEU
Harvard
Wheelock
Simmons
Size: Large
vs Small
1
1
1
0
0
Focus:
Research vs
Teaching
1
1
1
0
0
Co-ed vs.
women
0
0
0
0
1
Faculty:
Brilliant vs
Ordinary
0
0
1
0
1
Good food
vs. bad
0
1
1
0
1
Results
BU
NEU
Harvard
Wheelock
Simmons
Size: Large
vs Small
1
1
1
0
0
Focus:
Research vs
Teaching
1
1
1
0
0
Co-Ed vs.
Women
1
0
0
1
1
Faculty:
Brilliant vs
Ordinary
0
0
1
0
1
Good food
vs bad
0
1
1
0
1
• BU and NEU are nearly identical; further examination may
be necessary.
• Size and Research are equated - should they be or is this a
bias? Double counting this influence?
• Which constructs are most important to you?
What College Is Best For You?
What College Is Best For You?
Simmons!