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Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2013 Room 120 Integrated Learning Center (ILC) 10:00 - 10:50 Mondays, Wednesdays & Fridays . Welcome. http://www.youtube.com/watch?v=oSQJP40PcGI. Use this as your

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  1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall, 2013Room 120 Integrated Learning Center (ILC)10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

  2. Use this as your study guide By the end of lecture today9/20/13 • Characteristics of a distribution • Central Tendency • Dispersion • Shape • What are the three primary types of “measures of central • tendency”? • Mean • Median • Mode • Measures of variability • Range, Standard deviation and Variance • Memorizing the four definitional formulae

  3. Schedule of readings Before next exam (September 27th) Please read chapters 1 - 4 in Ha & Ha textbook Please read Appendix D, E & F onlineOn 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

  4. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  5. Homework due – Monday (September 23rd) On class website: please print and complete homework assignment # 8 Please double check – Allcell phones other electronic devices are turned off and stowed away

  6. Lab sessions Labs continue next week

  7. 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

  8. 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” Variability The larger the variability the wider the curve the larger the deviations scores tend to be The smaller the variability the narrower the curve the smaller the deviations scores tend to be Review

  9. Σ(x - x) = 0 Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 0” Mike Σ(x - µ) = ? Hunter 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” 5’8” 5’10” 6’0” 6’2” 6’4” Diallo How do we find the average height? = average height Σx N How do we find the average spread? Preston Σ(x - µ) = average deviation Σ(x - µ) = 0 N Review

  10. Σ(x - x) = 0 Σ(x - x) Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 0” Σ x - x = ? 2 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” 5’8” 5’10” 6’0” 6’2” 6’4” Square the deviations Σx Big problem N 2 Σ(x - µ) 2 Σ(x - µ) Σ(x - µ) = 0 N Review

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

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

  13. 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

  14. Standard deviation(definitional formula) - Let’s do one These are all deviation scores _ X - µ_ 1 - 5 = - 4 2 - 5 = - 3 3 - 5 = - 2 4 - 5 = - 1 5 - 5 = 0 6 - 5 = 1 7 - 5 = 2 8 - 5 = 3 9 - 5 = 4 0 (X - µ)2 16 9 4 1 0 1 4 9 16 60 Step 1: Find the mean _ X_ 1 2 3 4 5 6 7 8 9 45 ΣX = 45 ΣX / N = 45/9 = 5 Step 2:Subtract the mean from each score Step 3:Square the deviations Step 4:Find standard deviation a) 60 / 9 = 6.6667 This is the Variance! b) square root of 6.6667 = 2.5820 Σ(x - µ) = 0 This is the standard deviation!

  15. Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Note this is for population Fun Fact: Standard deviation squared = variance

  16. Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Note this is for sample Fun Fact: Standard deviation squared = variance

  17. Another example: How many kids in your family? 3 4 2 1 4 2 3 2 1 8

  18. Standard deviation - Let’s do one Definitional formula How many kids? Step 1: Find the mean X - µ_ 3 - 3 = 0 2 - 3 = -1 3 - 3 = 0 1 - 3 = -2 2 - 3 = -1 4 - 3 = 1 8 - 3 = 5 2 - 3 = -1 1 - 3 = -2 4 - 3 = 1 (X - µ)2 0 1 0 4 1 1 25 1 4 1 _ X_ 3 2 3 1 2 4 8 2 1 4 = 30 = 30/10 = 3 Step 2:Subtract the mean from each score (deviations) Step 3:Square the deviations Step 4:Add up the squared deviations Σ(x - µ) = 0 Step 5:Find standard deviation Σx = 30 Σ(x -µ)2 = 38 This is the Variance! a) 38 / 10 = 3.8 b) square root of 3.8 = 1.95 This is the standard deviation!

  19. Review of Homework Worksheet

  20. Review of Homework Worksheet 3 – 5 = -2 -22= 4 6 – 5 = +1 -2 1 3 -1 0 4 1 9 1 0 12= 1 3 -3 -1 1 -1 9 9 1 1 1 How many errors per hour? 50 36 0 36 = 2 2 10 - 1 5 4 4.5 6 .625 2 8

  21. Review of Homework Worksheet -12= 1 5 – 6 = -1 -1 2 -1 -1 3 1 4 1 1 9 22= 4 8 – 6 = +2 0 -1 3 1 -5 0 1 9 1 25 How many errors per hour? 60 0 52 52 6 errors 12 hours 2.4 = 2.4 10 - 1 5 5.5 6 .50 1 8 9

  22. Review of Homework Worksheet Must be complete and must be stapled

  23. Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David 0” Remember, it’s relative to the mean Generally, (on average) how far away is each score from the mean? Based on difference from the mean Mean Diallo Please memorize these Preston Shea Mike

  24. Variability Standard deviation: The average amount by which observations deviate on either side of their mean Based on difference from the mean Generally, (on average) how far away is each score from the mean? Remember, it’s relative to the mean Mean is 6’ Doug Chuck Irwin Raoul

  25. Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 What is the most common “deviation score”? Shea is 4 David is 0” Remember, We are thinking in terms of “deviations” 5’8” 5’10” 6’0” 6’2” 6’4”

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

  27. Deviation scores • 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 • 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 • 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? • Please write the formula for the standard deviation of a population • Please draw 3 curves showing 1, 2 & 3 standard deviations from mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David 0” How far away is each score from the mean? Mean Diallo Preston Shea Mike

  28. Thank you! See you next time!!

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