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

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 Characteristics of a distribution Central Tendency Dispersion Measures of variability Standard deviation Variance A note on notations Memorizing the four definitional formulae Empirical Rule for Normal Curve (68% vs 95% vs 99.7%)

Homework Assignment 7 & 8 Please complete the worksheet by hand Please complete the memorandum Due: Friday, February 3rd

Homework Assignment 7 & 8 Please complete the worksheet by hand Please complete the memorandum Due: Friday, February 3rd

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

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

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 David is 0” Diallo 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” Square the deviations Big problem Σ(x - x) 2 2 Σ(x - x) = 0 Σ(x - µ) N Σ(x - µ) 2 Σ(x - µ) = 0 Review

“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%

Summary of 7 facts to memorize

Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 z = -1 Mean = 50 σ = 10

Raw scores, z scores & probabilities 2 sd above and below mean 95% z = -2 z = +2 Mean = 50 σ = 10

Raw scores, z scores & probabilities 3 sd above and below mean 99.7% z = +3 z = -3 Mean = 50 σ = 10

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 Parameter mu – a mean Parameter X-bar – a mean - sample statistic S – standard deviation - sample statistic Distance from the mean in standard deviation units population Sigma squared and s squared - variance Sigma is parameter s is statistic Deviation scores x-µ is parameter x-x is statistic 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

Thank you! See you next time!!