Introduction to Statistics for the Social Sciences
SBS200 - Lecture Section 001, Spring 2017
Room 150 Harvill Building
9:00 - 9:50 Mondays, Wednesdays & Fridays.
http://www.youtube.com/watch?v=oSQJP40PcGI
http://www.youtube.com/watch?v=oSQJP40PcGI
Schedule of readings
Before next exam (March 3rd)
Please read chapters 1 - 8 in OpenStax textbook
Please read Chapters 10, 11, 12 and 14 in Plous
Chapter 10: The Representativeness Heuristic
Chapter 11: The Availability Heuristic
Chapter 12: Probability and Risk
Chapter 14: The Perception of Randomness
By the end of lecture today
2/20/17
Completing t-tests using Excel
Interpreting output
Preparing for Project 2
Approaches to probability:
Empirical, Subjective and Classical
On class website:
Please print and complete homework worksheet #12
Approaches to Probability and Dispersion.
Due: Wednesday, February 22nd
Everyone will want to be enrolled
in one of the lab sessions
Labs continue
With Project 2
t-tests
Using Excel
A word on “add-in”
Using Excel
?
What is probability
1. Empirical probability: relative frequency approach
Number of observed outcomes
Number of observations
Probability of getting into an educational program
Number of people they let in
Number of applicants
400
600
66% chance of
getting admitted
Probability of getting a rotten apple
Number of rotten apples
Number of apples
5% chance of
getting a rotten
100
apple
5
What is probability
1. Empirical probability: relative frequency approach
“There is a 20% chance
“More than 30% of the
10% of people who buy a
that a new stock
results from major
Number
of observed
house with
no pool build
offered in outcomes
an initial
search engines for the
one. What is the
public offering (IPO)
Number
observations
keyword phrase “ring
likelihood that
Bob will?of will
reach or exceed
tone” are fake
its target price on
Probability of hitting
the corvette pages created by
the first day.”
spammers.”
Number of carts that hit corvette
Number of carts rolled
182
200
= .91
91% chance of
hitting a corvette
2. Classic probability: a priori probabilities based on logic
rather than on data or experience.
All options are equally likely (deductive rather than inductive).
Likelihood get Chosen at
Lottery question right
random to be
on multiple team captain
choice test
Number of outcomes of specific event
Number of all possible events
In throwing a die what is the probability of getting a “2”
Number of sides with a 2
Number of sides
1
16% chance of
getting a two
= 6
In tossing a coin what is probability of getting a tail
Number of sides with a 1
Number of sides
1
=
2
50% chance
of getting a tail
3. Subjective probability: based on someone’s personal
judgment (often an expert), and often used when empirical
and classic approaches are not available.
Likelihood get a
60% chance
Likelihood
”B” in the class
that Patriots
that company
will play at
will invent
Super
Bowl
There
Verizon
new
type ofis a 5% chance that
battery with Sprint
merge
will
Bob says he is 90% sure he could swim across the river
Approach
Example
Empirical
There is a 2 percent chance of
twins in a randomly-chosen birth
Classical
There is a 50 % probability of
heads on a coin flip.
Subjective
There is a 5% chance that
Verizon will merge with Sprint
The probability of an event is the relative likelihood that
the event will occur.
The probability of event A [denoted P(A)], must lie
within the interval from 0 to 1:
0 < P(A) < 1
If P(A) = 0, then the
event cannot occur.
If P(A) = 1, then the event
is certain to occur.
The probabilities of all simple events must sum to 1
P(S) = P(E1) + P(E2) + … + P(En) = 1
For example, if the following number of purchases were made by
credit card:
32%
P(credit card) = .32
debit card:
20% Probability
P(debit card) = .20
cash:
35%
P(cash) = .35
check:
13%
P(check) = .13
Sum = 100%
Sum = 1.0
What is the complement of the probability of an event
The probability of event A = P(A).
The probability of the complement of the event A’ = P(A’)
• A’ is called “A prime”
Complement of A just means probability of “not A”
• P(A) + P(A’) = 100%
• P(A) = 100% - P(A’)
• P(A’) = 100% - P(A)
Probability of
getting a rotten apple
5% chance of “rotten apple”
95% chance of “not rotten apple”
100% chance of rotten or not
Probability of getting
into an educational program
66% chance of “admitted”
34% chance of “not admitted”
100% chance of admitted or not
Two mutually exclusive characteristics: if the occurrence of any
one of them automatically implies the non-occurrence of the
remaining characteristic
Two events are mutually exclusive if they cannot occur at the
same time (i.e. they have no outcomes in common).
Two propositions that logically cannot both be true.
Warranty
No
Warranty
For example, a car repair is
either covered by the
warranty (A) or not (B).
http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man
Satirical take on being “mutually exclusive”
Warranty
Recently a public figure in the heat of the
moment inadvertently made a statement that
reflected extreme stereotyping that many would
Arab
find highly offensive. It is within this context that
comical satirists have used the concept of
being “mutually exclusive” to have fun with the
statement.
No
Warranty
Decent ,
family man
Transcript:
Speaker 1:
“He’s an Arab”
Speaker 2:
“No ma’am, no ma’am.
He’s a decent, family
man, citizen…”
http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man
http://www.cc.com/video-clips/zec1b8/the-daily-show-with-jon-stewart-an-arab-family-man
Collectively Exhaustive Events
Events are collectively exhaustive if their union is
the entire sample space S.
Two mutually exclusive, collectively exhaustive
events are dichotomous (or binary) events.
Warranty
No
Warranty
For example, a car repair is
either covered by the
warranty (A) or not (B).