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

14.01

15.46

14.01

15.46

10.00

12.00

14.00

16.00

18.00

20.00

22.00

0 1 2 3 4

Significant Differences

14.01

15.46

14.01

15.46

10.00

12.00

14.00

16.00

18.00

20.00

22.00

0 1 2 3 4

Significant Differences

Detecting Deception

Do “lie detectors” really work?

Polygraph Test

0

10

20

30

40

50

60

70

80

90

Guilty people judged guilty Innocent people judged guilty

Percent

It works!

Polygraph Test

0

10

20

30

40

50

60

70

80

90

Guilty people judged guilty Innocent people judged guilty

Percent

Oops!

How Psychologists Judge Differences

The Mathematical Models

RH = P(“remember”|Old) ⎟⎠

⎞⎜⎝

⎛Φ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

′+′

′′Φ=

tC

Cdd

dd

tr

o

yx

yx

22

21

RF =P(“remem ber”|New) ( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

′+′

′−′Φ−Φ= r

yx

yxo C

dd

ddC

22

22

F = P(“old”|New) ( )oC−Φ=

H = P(“old”|Old)⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

′+′

′′Φ= o

yx

yx Cdd

dd

t 22

21

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 …

Fish ≻ Beef ?

Beef ≻ Fish ?

How is this possible?

• Beef ≻ Chicken

• Chicken ≻ Fish

• Fish ≻ Beef

What’s for dinner?

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

• Beef ≻ Chicken (Taste)

• Chicken ≻ Fish (Taste)

• Fish ≻ Beef (Health)

1 decision, but 2 dimensions

Two Dimensions

Beef

Chicken

Fish0

5

10

15

20

25

0 5 10 15 20 25

Health

Taste

Transitivity Within Dimension

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

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Multi-Dimensional Scaling

Repertory Grid (Kelly, 1955)

• Gather a set of schools you think you might be interested in

• Enumerate all possible triples

# Schools # Triples

3 1

4 3

5 6

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 0 1

Co-ed vs. women

0 0 1 0 0

Focus: Research vs

Teaching1 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)

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

Teaching1 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

Teaching1 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

Teaching1 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 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?

BU NEU Harvard Wheelock Simmons

Size: Large vs Small

1 1 1 0 0

Focus: Research vs

Teaching1 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

What College Is Best For You?

Simmons!

What College Is Best For You?