Introduction to Statistics for the Social Sciences SBS

Introduction to Statistics for the Social Sciences SBS 200, COMM 200, GEOG 200, PA 200, POL 200, or SOC 200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10: 00 - 10: 50 Mondays, Wednesdays & Fridays. http: //courses. eller. arizona. edu/mgmt/delaney/d 15 s_database_weekone_screenshot. xlsx

Hand out z tables

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

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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

Schedule of readings Before next exam (October 16 th) Please read chapters 1 - 8 in Open. Stax 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

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

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

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

Raw scores, z scores & probabilities Notice: 3 types of numbers z = • raw scores 2 • z scores • probabilities z= +2 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

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 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 10% of people who buy a that a new stock the results from Number of observed house with no pool build offered in outcomes an initial major search engines one. What is the public offering (IPO) Number observations for the keyword likelihood that Bob will? of will reach or exceed phrase “ring tone” are its target price on fake Probability of hitting the corvette the first day. ” pages created by 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 = 6 16% chance of getting a two 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(E 1) + P(E 2) + … + 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? video. Id=188474&title=an-arab-family-man

Collectively Exhaustive 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).

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? video. Id=188474&title=an-arab-family-man http: //www. cc. com/video-clips/zec 1 b 8/the-daily-show-with-jon-stewart-an-arab-family-man

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)

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. 5 A-25

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).

Probability of picking a Queen Probability of picking a Red 26/52 4/52 2/52 P(Q) = 4/52 (4 queens in a deck) P(R) = 26/52 (26 red cards in a deck) P(Q R) = 2/52 Probability of picking both R and Q P(Q R) = P(Q) + P(R) – P(Q R) = 4/52 + 26/52 – 2/52 = 28/52 =. 5385 or 53. 85% (2 red queens in a deck) 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 overstating the probability.

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)

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).