Lecture 10A: Generalizations

Business
1.  Podcast/Blog Reviews.
2.  Discuss ACA arguments.
3.  Generalizations



Generalizations
Definition: A generalization is the process of moving from some specific observations about individuals (or instances of a type of event) within a group to a general claim about members of the whole group (or instances of that type of event). 

Statistical Syllogism vs Enumerative Induction 

General Claims vs Universal Claims:  
Universal claims are guarantees:  E.g. All ravens are black, I always eat peanut butter and toast for breakfast, Everytime I see you falling I get down on my knees and pray...   
General claims are probabilistic:  E.g., 76% of SNAP households included a child, an elderly person, or a disabled person. These vulnerable households receive 83% of all SNAP benefits 
http://www.fns.usda.gov/ora/menu/Published/snap/SNAPPartHH.htm
Most UNLV students like pizza, only a small portion of the Vegas population has been to Panama, only about 1/3 of all students who begin 2 year degrees complete them within 3 years.

Mini Phil of Science Problem:  How big of a sample do you need? (Drug test vs Stove is hot).

Examples of Generalizations
spurious causation

A
Informal Presentation:  10% of Ami's students are wearing red today therefore around 10% of UNLV students must be wearing red today.

Formal Structure
(P1)  The students in Ami's class are representative of all UNLV students.
(P2)  10% of the students in Ami's class are wearing red today.
(C)    Therefore around 10% of UNLV students must be wearing red today.

B
75% of my friends at school have student loans therefore 75% of students at UNLV have student loans.

C
All my friends have happier and more interesting lives than mine.  Every time I check my facebook feed, they're posting about doing something interesting or fun.  My life sucks.

D
Conrad Hilton started out dirt poor and became super-rich, therefore anyone can do it.

E
We asked anyone who was motivated to lose weight to try our new magic diet of eating only natural organic birch tree bark.  Over 80% of participants lost weight.  80% of people who try our new magic diet will lose weight. 

E  
Fox just did a call-in telephone poll of over 10 000 people and 80% of them agreed that Obama is doing a terrible job.  That shows that around 80% of Americans think Obama's doing a horrible job.

F 
If you're sick you should use this homeopathic remedy.  It worked for me last time I was sick.

H  
1/3 of students in two-year programs at Washington State community colleges graduate within 3 years.  Therefore, about 30% of people in 2 year programs graduate within 3 years

G
Trolly Dilemma (from 2:00) and fMRI:  People who make the utilitarian choice are better moral reasoners.  +What is the fMRI measuring?

H
In the ultimatum game, most studies in the best American universities have shown that most subjects offer between 30 to 50% and will usually reject anything below around 30%. Therefore, the human notion of fairness is that when playing the ultimatum game, you should give 30-50% to be fair.

I
http://tylervigen.com/view_correlation?id=677
spurious correlations

J

K. Putting it all together:
Diet soda and gut bacteria








Americans Are WIERD (Western, Educated, Industrialized, Rich, and Democratic)
Ultimatum Game: Americans vs Machiguenga vs Gift Giving Cultures vs standard game theoretic model (Homo economicus)
"[...] their goal was not to say that one culturally shaped psychology was better or worse than another—only that we’ll never truly understand human behavior and cognition until we expand the sample pool beyond its current small slice of humanity. "

"At its heart, the challenge of the WEIRD paper is not simply to the field of experimental human research (do more cross-cultural studies!); it is a challenge to our Western conception of human nature."


Interesting Generalizations
Veterans and Homelessness
Homelessness Stats

Tipping

What property are we measuring?
race and private prisons

Key Concepts
Structure of Generalizations
(P1)  S is a sample of Xs.
(P2)  Proportion 1 of Xs in S are Y.
(C)   Proportion 2 of Xs  are Y. 

Structure of Statistical Syllogism
(P1)  Proportion 1 of Xs are Y.
(P2)  S is a sample of Xs.
(C)   Proportion 2 of Xs in S are Y.

Target Group/Population: The whole group of things the generalization is about.
Sample:  The observed of selected members of the whole target group.
Relevant Property:  The property of the group we are studying.
Representativeness: The degree to which the sample resembles--in relevant ways--the target group.

How to Analyze/Criticize a Generalization: Like all inductive arguments, generalizations can range from anywhere between weak and strong.  Its strength will depend on how well it passes the following tests:
(a)  Is the sample size large enough?  If not, then it is a hasty generalization.  Arguments using anecdotal evidence commit this fallacy. 
(b)  Is the sample representative of the group?  I.e., Does the sample have all the same relevant characteristics of the target group? If not then there is sample bias. Volunteer subjects in a study may not be representative of the population being studied, as a consequence, the results of the study may not be generizable to the entire population.
(c)  Does the way the sample was selected cause bias (I.e., non-randomly)?  If yes, then there is selection bias:  SELECTION BIAS: occurs when the subject CHOOSES whether to enter a drug group or a placebo group rather than being randomly assigned. OR, the investigator purposely CHOOSES to put a subject in a drug or placebo group.
(d)  Is the property being attributed to the sample actually the property being measured?  (I.e., Do Xs really have property Y?)  If not then there's a measurement problem.

For statistical syllogisms:
(a)  Is S representative of X? 
(b)  Is the variation in concentrations of properties across Xs. (Distribution)
(c)  Are there important subdivisions of X (the target group).

Homework 10A
P. 232 Ex 9A  Do Q1 Pick any 4; Q2 all
Learn from the pros:  Read: Effects of Diet Soda on Gut Bacteria