Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. February 4 http://www.youtube.com/watch?v=oSQJP40PcGI
Even if you have not yet registered your clicker you can still participate The Green Sheets
Schedule of readings Before next exam (February 8) 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
Labs continue this week 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 Review
How far away is each score from the mean? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores (x - µ) Deviation scores: The amount by which observations deviate on either side of their mean (x - µ) How far away is each score from the mean? Mean Diallo Deviation score Mike Preston Shea (x - µ) = ? Hunter 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” Diallo How do we find each deviation score? (x - µ) Preston Hunter Diallo Mike Preston Find distance of each person from the mean (subtract their score from mean) Review
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” Add up Deviation scores 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” How do we find the average height? N Σx = average height How do we find the average spread? Σ(x - x) = 0 Σ(x - µ) N Won’t Work = average deviation Σ(x - µ) = 0 Review
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
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 Review
You know by heart – you’ve memorized Standard deviation: The average amount by which observations deviate on either side of their mean “Sum of Squares” You know by heart – you’ve memorized these formula Review
You know by heart – you’ve memorized Standard deviation: The average amount by which observations deviate on either side of their mean “degrees of freedom” You know by heart – you’ve memorized these formula Review
Standard deviation squared = variance Standard deviation: The average amount by which observations deviate on either side of their mean Both are called “standard deviation” Both are called “variance” What do these two formula have in common? Standard deviation squared = variance Fun Fact:
Standard deviation: The average amount by which observations deviate on either side of their mean Both are for sample Both are for population 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? Review
Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve Review
Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve 68% 95% 99.7% Review
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
Summary of 7 facts to memorize
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
Homework Assignment # 7 Due: Wednesday, February 6 Worksheet with Memorandum Due: Wednesday, February 6
Step 2 Find each deviation score Step 1 Find the mean Step 2 Find each deviation score Step 3 Square each deviation score and add them up Step 4 Divide by n and take square root
Preview 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
Preview 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 6 5.5 5 1 9 8
Homework Assignment # 7 Due: Wednesday, February 6 Worksheet with Memorandum Due: Wednesday, February 6
Thank you! See you next time!!