2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx

3. Hand out z tables

4. Everyone will want to be enrolled in one of the lab sessions Labs continue this week, Project 1

7. Please re-register your clicker http://student.turningtechnologies.com/

8. By the end of lecture today 10/5/15 Connecting raw scores, and z scores to probability, proportion and area of curve Percentiles Approaches to probability: Empirical, Subjective and Classical

9. Before next exam (October 16th) 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 Schedule of readings

10. Homework Assignment Assignment 9 - Extension Please complete this homework worksheet Finding z scores and areas under the curve Due: Monday, October 5th Extended deadline to Wednesday, October 7 th Homework Assignment Assignment 10 Please complete this homework worksheet Approaches to Probability and Dispersion Due: Wednesday, October 7 th

11. Raw Scores (actual data) Distance from the mean (z scores) Proportion of curve (area from mean) convert We care about this! “percentiles” “percent of people” “proportion of curve” “relative position” We care about this! What is the actual number on this scale? “height” vs “weight” “pounds” vs “test score” Raw Scores (actual data) Distance from the mean (z scores) Proportion of curve (area from mean) convert Raw scores, z scores & probabilities z = -1z = 1 68% z = -1z = 1 68%

12. Raw Scores Area & Probability Z Scores Formula z table Have raw score Find z Have z Find raw score Have area Find z Have z Find area Normal distribution Raw scores z-scores probabilities

13. Notice: 3 types of numbers raw scores z scores probabilities Mean = 50 Standard deviation = 10 If we go up two standard deviations z score = +2.0 and raw score = 70 If we go down two standard deviations z score = -2.0 and raw score = 30 Raw scores, z scores & probabilities z = -2 z = +2

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

15. What is probability 1. Empirical probability: relative frequency approach Number of observed outcomes Number of observations Probability of hitting the corvette Number of carts that hit corvette Number of carts rolled 182 200 91% chance of hitting a corvette =.91 10% of people who buy a house with no pool build one. What is the likelihood that Bob will? “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.”

16. 2. Classic probability: a priori probabilities based on logic rather than on data or experience. All options are equally likely (deductive rather than inductive). 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 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 1 6 16% chance of getting a two = = Lottery Likelihood get question right on multiple choice test Chosen at random to be team captain

17. 3. Subjective probability: based on someone’s personal judgment (often an expert), and often used when empirical and classic approaches are not available. There is a 5% chance that Verizon will merge with Sprint Bob says he is 90% sure he could swim across the river 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

18. 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

19. 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.

20. The probabilities of all simple events must sum to 1 For example, if the following number of purchases were made by P(S) = P(E 1 ) + P(E 2 ) + … + P(E n ) = 1 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

21. 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 into an educational program 66% chance of “admitted” 34% chance of “not admitted” 100% chance of admitted or not 5% chance of “rotten apple” Probability of getting a rotten apple 95% chance of “not rotten apple” 100% chance of rotten or not

22. Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic 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. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-manWarranty No Warranty For example, a car repair is either covered by the warranty (A) or not (B).

23. Events are collectively exhaustive if their union is the entire sample space S. Events are collectively exhaustive if their union is the entire sample space S. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. 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). Warranty No Warranty Collectively Exhaustive Events

24. Satirical take on being “mutually exclusive” 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. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man Transcript: Speaker 1: “He’s an Arab” Speaker 2: “No ma’am, no ma’am. He’s a decent, family man, citizen…” Arab Decent, family man Warranty No Warranty http://www.cc.com/video-clips/zec1b8/the-daily-show-with-jon-stewart-an-arab-family-man

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

26. 5A-25 union 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.

27. What is probability of drawing a red card or a queen? It is the possibility of drawing It is the possibility of drawing either a queen (4 ways) or a red card (26 ways) or both (2 ways). either a queen (4 ways) or a red card (26 ways) or both (2 ways). what is Q  R? union 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”).

28. P(Q) = 4/52 (4 queens in a deck) = 4/52 + 26/52 – 2/52 P(Q  R) = P(Q) + P(R) – P(Q  R) = 28/52 =.5385 or 53.85% P(R) = 26/52 (26 red cards in a deck) P(Q  R) = 2/52 (2 red queens in a deck) Probability of picking a Queen Probability of picking a Red Probability of picking both R and Q 4/52 26/52 2/52 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.

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

30. what is Q  R? 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? It is the possibility of drawing both a queen and a red card (2 ways).