Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10: :50 Mondays, Wednesdays & Fridays.

Labs continue this week

Schedule of readings Before next exam (September 26 th ) Please read chapters in Ha & Ha textbook Please read Appendix D, E & F online On syllabus this is referred to as online readings 1, 2 & 3 Please read Chapters 1, 5, 6 and 13 in Plous Chapter 1: Selective Perception Chapter 5: Plasticity Chapter 6: Effects of Question Wording and Framing Chapter 13: Anchoring and Adjustment

Reminder A note on doodling

By the end of lecture today 9/22/14 Use this as your study guide Characteristics of a distribution Central Tendency Dispersion Primary types of “measures of central tendency”? Mean Median Mode Measures of variability Range Standard deviation Variance Memorizing the four definitional formulae

Homework due – Wednesday (September 22 nd ) Assignment 8 Please read Chapter 4 in our regular Ha & Ha textbook (Renee Ha & James Ha are the authors). Please answer the questions (page 66-68) Due: Wednesday, September 24th

Exam 1 – This Friday – September 26 th Study Guide is online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

Review – Pop Quiz 1. What does this symbol refer to? 2. What does this symbol refer to? 5. What does this symbol refer to? 3. What does this symbol refer to? 4. What does this symbol refer to? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? The standard deviation (population) The mean (population) The mean (sample) The standard deviation (sample) Each individual score sigma population mu x-bar population sample s

6. What does this refer to? 7. What does this refer to? 8. What do these two refer to? 9a. What does this refer to? What are they called? How are they different What is it called? Use it for sample data or population? What are they called? What do they refer to? How are they different What are they called? How are they different Variance population sample Sigma squared S squared Deviation scores population sample Sum of squares population sample Degrees of freedom sample Review – Pop Quiz

9b. What does this refer to? What are they called? What do they refer to? How are they different 10. What does this refer to? What are they called? What do they refer to? How are they different Variance population sample Standard Deviation population sample

Standard deviation: The average amount by which observations deviate on either side of their mean Based on difference from the mean Mean Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David 0” Preston is 2” Deviation scores Mike Shea Preston Diallo Generally, (on average) how far away is each score from the mean? Remember, it’s relative to the mean Please memorize these “Sum of Squares” “n-1” is “Degrees of Freedom” “n-1” is “Degrees of Freedom” Remember, We are thinking in terms of “deviations”

Review of Homework Worksheet

– 5 = – 5 = = = = Review of Homework Worksheet

– 6 = – 6 = = = = Preview of Homework Worksheet.

Review of Homework Worksheet Must be complete and must be stapled

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

Let’s estimate some standard deviation values Standard deviation is a ‘spread’ score We’re estimating the typical distance score (distance of each score from the mean)

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency What’s the ‘typical’ or standard deviation? Standard Deviation = 3.5

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $47 What’s the largest possible deviation? Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0 Deviation scores $47 – $37 = $10 What is the least common “deviation scores”? What is the most common score? What is the most common “deviation score”? Deviation = 0 $27 – $37 = -$10

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $47 What is the deviation score for $38? Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 Deviation scores Deviation = 1

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $39? Deviation = 2

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 1,1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $40? Deviation = 3

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 1,1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $41? Deviation = 4

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 1,1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $42? Deviation = 5

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 1,1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $43? Deviation = 6

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 1,1,1,1,1,1,1,1,1 Deviation scores What is the deviation score for $44? Deviation = 7

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 1,1,1,1,1,1,1,1,1 Deviation scores Deviation = 8 What is the deviation score for $45?

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 1,1,1,1,1,1,1,1,1 Deviation scores Deviation = 9 What is the deviation score for $46?

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 1,1,1,1,1,1,1,1,1 Deviation scores Deviation = 10 What is the deviation score for $46?

Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) Mean = $37 Range = $27 - $ Price per Movie Package Frequency 0,0,0,0,0,0,0,0,0,0 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 1,1,1,1,1,1,1,1,1 Deviation scores Estimate Average Deviation Score What’s the ‘typical’ or standard deviation? Standard Deviation = 3.5

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

Mean = 1700 pounds Range = 1200 – 2100 What’s the ‘typical’ or standard deviation? Standard Deviation = 200 Pounds of pressure to break casing on an insulator (We applied pressure until the insulator casing broke) What’s the largest possible deviation? 1200 – 1700 = – 1700 = 400

Amount of Bonuses (based on commission) We sampled 100 retail workers Mean = $50 Range = $25 - $75 What’s the largest possible deviation? What’s the ‘typical’ or standard deviation? Standard Deviation = 10 $75 – $50= $25 $25 – $50= -$25

Waiting time for service at bank We sampled 100 banks (From time entering line to time reaching teller) Mean = 3 minutes Range = What’s the largest possible deviation? What’s the ‘typical’ or standard deviation? Standard Deviation = – 3.0= – 3.0= -.8

Scores, standard deviations, and probabilities Actually Actually To be exactly 95% we will use z = 1.96

Mean = 3 kids Range = What’s the ‘typical’ or standard deviation? Standard Deviation = 1.7 Number of kids in family We sampled 100 families (counted number of kids) What’s the largest possible deviation? 1 - 3= -2 8 – 3= 5

Mean = 80 Range = What’s the ‘typical’ or standard deviation? Standard Deviation = 10 Number correct on exam We tested 100 students (counted number of correct on 100 point test) What’s the largest possible deviation? = = -25

Let’s try one Standard Deviation = 27 Monthly electric bills for 50 apartments (amount of dollars charged for the month) 150 – 213 = – 97 = 53 Mean = $150 Range = What’s the largest possible deviation? The best estimate of the population standard deviation is a. $150 b. $27 c. $53 d. $63

Let’s try one Standard Deviation = Amount of soda in 2-liter containers (measured amount of soda in 2-liter bottles) The best estimate of the population standard deviation is a b c d. 2.0 Mean = 2.0 Range = – What’s the largest possible deviation? 2 – = – =

Let’s try one Standard Deviation = 10 Scores on an Art History exam (measured number correct out of 100) The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d..5 Mean = 50 Range = What’s the largest possible deviation? = = - 25

Let’s try one Standard Deviation = 10 Scores on Art History Exam The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d..5 Mean = 50 Range = One way to estimate standard deviation* σ≈ range / 6 45 / 6 = 7.5

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

Writing Assignment: 1. What is a “deviation score” 2. Preston has a deviation score of 2: What does that tell us about Preston? Is he taller or shorter than the mean? And by how much? Are most people in the group taller or shorter than Preston 3.Mike has a deviation score of -4: What does that tell us about Mike? Is he taller or shorter than the mean? And by how much? Are most people in the group taller or shorter than Mike 4.Diallo has a deviation score of 0: What does that tell us about Diallo? Is he taller or shorter than the mean? And by how much? Are most people in the group taller or shorter than Diallo? 5.Please write the formula for the standard deviation of a population 6.Please draw 3 curves showing 1, 2 & 3 standard deviations from mean Mean Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David 0” Preston is 2” Deviation scores Mike Shea Preston Diallo How far away is each score from the mean?