Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered Row A 15 14 Row A 13 12 11 10 9 8 7 6 5 4 3 2 1 Row A Row B 23 22 21 20 Row B 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row B Row C 25 24 23 22 21 Row C 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row C Row D 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Row F 35 34 33 32 31 30 29 28 27 26 Row F 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 35 34 33 32 31 30 29 28 27 26 Row G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 Row H 12 11 10 9 8 7 6 5 4 3 2 1 Row H 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 Row J 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J 41 40 39 38 37 36 35 34 33 32 31 30 29 Row K 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row K Row L 33 32 31 30 29 28 27 26 25 Row L 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 21 20 19 Row M 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row P 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Harvill 150 renumbered table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk

Schedule of readings Before next exam (September 22nd) Please read chapters 1 - 5 in OpenStax textbook Please read Appendix D online On syllabus this is referred to as online readings 1 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

writing assignment forms notebook and clickers to each lecture Remember bring your writing assignment forms notebook and clickers to each lecture

Even if you have not yet registered your clicker you can still participate

Labs continue next week Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue next week Exam 1 Review

Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric

Based on difference from the mean Deviation scores: The amount by which each observation deviates from the mean (above or below) Deviation scores Diallo is 0” (x - µ) Preston is 2” Mike is -4” Hunter is -2 Standard deviation: The average amount by which observations deviate on either side of their mean Shea is 4 David is 0” Remember It’s relative to the mean 5’8” 5’10” 6’0” 6’2” 6’4” Based on difference from the mean

How far away is each score from the mean? Standard deviation: The average amount by which observations deviate on either side of their mean Deviation scores (x - µ) Diallo is 0” Preston is 2” How far away is each score from the mean? Mike is -4” Hunter is -2 Shea is 4 Mean Step 1 Find the mean David is 0” Diallo Step 2 Find each deviation score Preston Σ (x - µ) = ? Shea Mike 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Step 3 Square each deviation score And add them up Step 4 Divide by n and take square root Σ(x - x) 2 2 Σ(x - x) = 0 Σ(x - µ) N Σ(x - µ) 2 Σ(x - µ) = 0

These would be helpful to know by heart – please memorize Standard deviation: The average amount by which observations deviate on either side of their mean These would be helpful to know by heart – please memorize these formula

What do these two formula have in common? Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common?

What do these two formula have in common? Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common?

How do these formula differ? Standard deviation: The average amount by which observations deviate on either side of their mean “n-1” is Degrees of Freedom” How do these formula differ?

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

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

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve 68% 95% 99.7%

These would be helpful to know by heart – please memorize areas 1 sd above and below mean 68% 2 sd above and below mean 95% 3 sd above and below mean 99.7% These would be helpful to know by heart – please memorize areas

Summary of 7 facts to memorize

We estimated and calculated the standard deviation Now let’s use it as a measure of counting

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

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, hand it in now

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

Thank you! See you next time!!