1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. By the end of lecture today 10/17/16
Approaches to probability:
Empirical, Subjective and Classical
Law of Large Numbers
Central Limit Theorem

4. Before next exam (November 18th)
Please read chapters in OpenStax textbook
Please read Chapters 2, 3, and 4 in Plous
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

5. Homework
On class website:
Please print and complete homework worksheet #12
Approaches to Probability and Dispersion.
Due: Wednesday, October 19th
Preview

6. .
Homework
On class website:
Please print and complete homework worksheet #12
Approaches to Probability and Dispersion.
Due: Wednesday, October 19th
Preview
.1915
.3944
.4332
.3944
.3944
.2029 44 50 55 50 55 52 55 4 =
-1.5 4 4 =
+.5 =
+1.25
z of 1.5 = area of .4332
z of .5 = area of .1915
1.25 = area of .3944 4 4 =
+1.25 =
+1.25
= .1056
z of 1.25 = area of .3944
z of 1.25 = area of .3944
= .8276
= .2029

7. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
With Project 1
Presentations

8. Presentation Skills

9. Presentation Skills

10. Presentation Skills

11. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
With Project 1
Presentations

13. 66% chance of getting admitted
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
400
66% chance of getting admitted
Number of applicants
600
Probability of getting a rotten apple
Number of rotten apples 5
5% chance of
getting a rotten
apple
Number of apples
100

14. 1. Empirical probability: relative frequency approach
What is probability
1. Empirical probability: relative frequency approach
“There is a 20% chance that a new stock offered in an initial public offering (IPO) will reach or exceed
its target price on the first day.”
“More than 30% of the results from major search engines for the keyword phrase “ring tone” are fake
pages created by spammers.”
10% of people who buy a house with no pool build one. What is the likelihood that Bob will?
Number of observed outcomes
Number of observations
Probability of hitting the corvette
Number of carts that hit corvette
Number of carts rolled
182
= .91
200
91% chance of hitting a corvette

15. = = 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 question right on multiple choice test
Chosen at random to be team captain
Lottery
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 1
16% chance of getting a two =
Number of sides 6
In tossing a coin what is probability of getting a tail
Number of sides with a 1 1
50% chance
of getting a tail =
Number of sides 2

16. 3. Subjective probability: based on someone’s personal
judgment (often an expert), and often used when empirical
and classic approaches are not available.
Likelihood that company will invent new type of battery
Likelihood get a ”B” in the class
60% chance that Patriots will play at Super Bowl
There is a 5% chance that Verizon will
merge with Sprint
Bob says he is 90% sure he could swim across the river

17. Approach Example Empirical Classical Subjective
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

18. The probability of event A [denoted P(A)], must lie
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.

19. 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%
debit card:
20%
cash:
35%
check:
13%
Sum =
100%
P(credit card) =
.32
P(debit card) =
.20
P(cash) =
.35
P(check) =
.13
Sum =
1.0
Probability

20. Probability of getting into an educational program
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

21. 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.
No Warranty
Warranty
For example, a car repair is either covered by the warranty (A) or not (B).

22. Satirical take on being “mutually exclusive”
No Warranty
Warranty
Recently a public figure in the heat of the moment inadvertently made a statement that reflected extreme stereotyping that many would 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.
Decent ,
family man
Arab
Transcript:
Speaker 1:
“He’s an Arab”
Speaker 2:
“No ma’am, no ma’am.
He’s a decent, family
man, citizen…”

23. 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.
For example, a car repair is either covered by the warranty (A) or not (B).
No Warranty
Warranty

24. ∩ Union versus Intersection Union of two events means
Event A or Event B will happen ∩
P(A B)
Intersection of two events means
Event A and Event B will happen
Also called a “joint probability”
P(A ∩ B)

25. The union of two events: all outcomes in the
sample space S that are contained either in event
A or in event B or both (denoted A  B or “A or B”).
 may be read as “or” since one or the other or both events may occur.

26. The union of two events: all outcomes contained either in event A or in event B or both (denoted A  B or “A or B”).
What is probability of drawing a red card or a queen?
what is Q  R?
It is the possibility of drawing
either a queen (4 ways) or a red card (26 ways) or both (2 ways).

27. P(Q) = 4/52 (4 queens in a deck) 2/52
Probability of picking a Queen
Probability of picking a Red
4/52
26/52
P(Q) = 4/52 (4 queens in a deck)
2/52
P(R) = 26/52
(26 red cards in a deck)
P(Q  R) = 2/52
(2 red queens in a deck)
Probability of picking both
R and Q
When you add the P(A) and P(B) together, you count the P(A and B) twice. So, you have to subtract P(A  B) to avoid over-stating the probability.
P(Q  R) = P(Q) + P(R) – P(Q  R)
= 4/ /52 – 2/52
= 28/52 = or 53.85%

28. ∩ Union versus Intersection Union of two events means
Event A or Event B will happen ∩
P(A B)
Intersection of two events means
Event A and Event B will happen
Also called a “joint probability”
P(A ∩ B)

29. The intersection of two events: all outcomes contained in both event A and event B (denoted A  B or “A and B”)
What is probability of drawing red queen?
what is Q  R?
It is the possibility of drawing both a queen and a red card (2 ways).

30. Thank you!
See you next time!!