Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

Do not hand it in until it: Is correct, complete and stapled Homework Assignment 7 & 8 Please complete the worksheet by hand Please complete the memorandum Due: Friday, February 6th Do not hand it in until it: Is correct, complete and stapled If it is not complete and correct, consider this an “extension” and hand it in next time

Review of Homework Worksheet Each of these are deviation scores 3 – 5 = -2 -22= 4 6 – 5 = +1 -2 1 3 -1 4 1 9 12= 1 3 -3 -1 1 9 1 Σ(x - µ) = 0 50 36 36 2 = 2 10 - 1 This is the standard deviation! 5 4 4.5 2 8 6

Review of Homework Worksheet -12= 1 5 – 6 = -1 -1 2 3 1 4 9 22= 4 8 – 6 = +2 -1 3 1 -5 1 9 25 60 52 52 2.4 = 2.4 10 - 1 5 6 5.5 1 9 8

If it is complete and correct, hand it in now Homework Assignment 7 & 8 Please complete the worksheet by hand Please complete the memorandum Due: Friday, February 6th If it is complete and correct, hand it in now Do not hand it in until it: Is correct, complete and stapled If it is not complete and correct, consider this an “extension” and hand it in next time

A note on doodling

Schedule of readings Before next exam (February 10) Please read chapters 1 - 5 in OpenStax 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

By the end of lecture today 2/1/17 Use this as your study guide By the end of lecture today 2/1/17 Measures of variability Range Standard deviation Variance Memorizing the four definitional formulae z-scores

Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue next week

Writing Assignment – Pop Quiz

Writing Assignment – Pop Quiz

Writing Assignment – Pop Quiz Distance from the mean X Taller 2 inches Preston is 2” taller than the mean (taller than most) Taller 2 inches Shorter X Mike is 4” shorter than the mean (shorter than most) Shorter 4 inches Taller X Equal to mean Diallo is exactly same height as mean (half taller half shorter) 0 inches Half are Shorter

Writing Assignment – Pop Quiz Sigma – standard deviation - population Parameter mu – a mean – an average - population Parameter x-bar – a mean – an average - sample statistic s – standard deviation - sample statistic The number of “standard deviations” the score is from the mean population Sigma squared and s squared - variance Sigma is parameter (population) s is statistic (sample) Deviation scores (x-µ) for population (parameter) (x-x) is statistic (sample) Sum of squares On left is statistic on right is parameter Standard deviation s is statistic sigma is parameter Degrees of freedom sample

If it is complete and correct, hold on to it for your own reference

Summary of 7 facts to memorize

z score = raw score - mean standard deviation If we go up one standard deviation z score = +1.0 and raw score = 105 z = -1 z = +1 68% If we go down one standard deviation z score = -1.0 and raw score = 95 85 90 95 100 105 110 115 If we go up two standard deviations z score = +2.0 and raw score = 110 z = -2 95% z = +2 If we go down two standard deviations z score = -2.0 and raw score = 90 85 90 95 100 105 110 115 If we go up three standard deviations z score = +3.0 and raw score = 115 99.7% z = -3 z = +3 If we go down three standard deviations z score = -3.0 and raw score = 85 85 90 95 100 105 110 115 z score: A score that indicates how many standard deviations an observation is above or below the mean of the distribution z score = raw score - mean standard deviation

Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 z = -1 Mean = 50 σ = 10 If we go up one standard deviation z score = +1.0 and raw score = 60 If we go down one standard deviation z score = -1.0 and raw score = 40

Raw scores, z scores & probabilities 2 sd above and below mean 95% z = -2 z = +2 Mean = 50 σ = 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 3 sd above and below mean 99.7% z = +3 z = -3 Mean = 50 σ = 10 If we go up three standard deviations z score = +3.0 and raw score = 80 If we go down three standard deviations z score = -3.0 and raw score = 20

z score = raw score - mean standard deviation If we go up one standard deviation z score = +1.0 and raw score = 105 z = -1 z = +1 68% If we go down one standard deviation z score = -1.0 and raw score = 95 85 90 95 100 105 110 115 If we go up two standard deviations z score = +2.0 and raw score = 110 z = -2 95% z = +2 If we go down two standard deviations z score = -2.0 and raw score = 90 85 90 95 100 105 110 115 If we go up three standard deviations z score = +3.0 and raw score = 115 99.7% z = -3 z = +3 If we go down three standard deviations z score = -3.0 and raw score = 85 85 90 95 100 105 110 115 z score: A score that indicates how many standard deviations an observation is above or below the mean of the distribution z score = raw score - mean standard deviation

Price per Movie Package Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) What is the most common “deviation score”? 12 Deviation = 0 10 Frequency 8 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package This distance is about 3 - 4 points on number line What’s the ‘typical’ or standard deviation? Mean = $37 Range = $27 - $47 Standard Deviation = 3.5

Amount of Bonuses (based on commission) We sampled 100 retail workers 68% 95% 99.7% What’s the ‘typical’ or standard deviation? This distance is about 10 points on number line What’s the largest possible deviations? Mean = $50 Range = $25 - $75 $75 – $50= $25 $25 – $50= -$25 Standard Deviation = 10

Pounds of pressure to break casing on an insulator (We applied pressure until the insulator casing broke) What’s the ‘typical’ or standard deviation? This distance is about 200 points on number line Mean = 1700 pounds Range = 1200 – 2100 What’s the largest possible deviation? 2100-1700 = 400 Standard Deviation = 225 1200-1700 = -500

Waiting time for service at bank We sampled 100 banks (From time entering line to time reaching teller) What’s the ‘typical’ or standard deviation? This distance is about Around .3 points on number line Mean = 3 minutes Range = 2.4- 3.6 What’s the largest possible deviation? 3.6-3.0=.6 2.4-3.0=-.6 Standard Deviation = 0.34

Number correct on exam (counted number of correct on 100 point test) Mean = 50 Standard Deviation = 10

Quiz: Just for fun Monthly electric bills for 50 apartments (amount of dollars charged for the month) Mean = $150 Range = 95 - 205 The best estimate of the population standard deviation is a. $150 b. $25 c. $50 d. $63 Standard Deviation = 25

Quiz: Just for fun Amount of soda in 2-liter containers (measured amount of soda in 2-liter bottles) What’s the largest possible deviation? Mean = 2.0 Range = 1.8 – 2.25 0.25 -0.20 The best estimate of the population standard deviation is a. 0.1 b. 0.2 c. 0.3 d. 2.0 Standard Deviation = 0.1

Scores on an Art History exam (measured number correct out of 100) Quiz: Just for fun Scores on an Art History exam (measured number correct out of 100) What’s the largest possible deviation? Mean = 50 Range = 30 - 70 25 - 50= - 20 70 - 80 = 20 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

Scores on an Art History exam (measured number correct out of 100) Quiz: Just for fun Scores on an Art History exam (measured number correct out of 100) Mean = 50 Range = 30 - 70 One way to estimate standard deviation* σ≈ range / 5 Range 70 – 30 = 40 40 / 5 = 8 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

Scores, standard deviations, and probabilities The normal curve always has the same shape. They differ only by having different means and standard deviation

Thank you! See you next time!!