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Introduction to Statistics for Social Sciences - Fall 2015 Lecture Section 001

This is an introductory course to statistics for social sciences, covering topics such as raw scores, z-scores, probability, and the normal distribution.

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Introduction to Statistics for Social Sciences - Fall 2015 Lecture Section 001

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  1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall 2015Room 150 Harvill Building10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx

  2. z tables

  3. Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue this week, Project 1

  4. Please re-register your clicker http://student.turningtechnologies.com/

  5. By the end of lecture today10/7/15 Connecting raw scores, and z scores to probability, proportion and area of curve Percentiles Approaches to probability: Empirical, Subjective and Classical

  6. Schedule of readings Before next exam (October 16th) Please read chapters 1 - 8 in OpenStax textbook Please read Chapters 10, 11, 12 and 14 in Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

  7. Homework Assignment Assignment 9 - Extension Please complete this homework worksheet Finding z scores and areas under the curve Due: Monday, October 5th Extended deadline to Wednesday, October 7th Homework Assignment Assignment 10 Please complete this homework worksheet Approaches to Probability and Dispersion Due: Wednesday, October 7th

  8. Raw scores, z scores & probabilities Distance from the mean (z scores) convert convert Proportion of curve (area from mean) Raw Scores (actual data) 68% We care about this! What is the actual number on this scale?“height” vs “weight” “pounds” vs “test score” We care about this! “percentiles” “percent of people” “proportion of curve” “relative position” z = -1 z = -1 z = 1 z = 1 68% Proportion of curve (area from mean) Raw Scores (actual data) Distance from the mean (z scores) convert convert

  9. Normal distribution Raw scores z-scores probabilities Z Scores Have z Find raw score Have z Find area z table Formula Have area Find z Area & Probability Raw Scores Have raw score Find z

  10. Raw scores, z scores & probabilities • Notice: • 3 types of numbers • raw scores • z scores • probabilities Mean = 50 Standard deviation = 10 z = -2 z = +2 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

  11. Always draw a picture! Homework worksheet

  12. Homework worksheet .6800 1 also fine: 68.00% also fine: .6826 .6800 1 sd 1 sd z = 1 z =-1 30 32 28

  13. Homework worksheet .9500 2 also fine: 95.00% also fine: .9544 .9500 2 sd 2 sd z =-2 z = 2 26 34 30 32 28

  14. Homework worksheet .9970 3 also fine: 99.70% also fine: .9974 .9970 3 sd 3 sd z =-3 z = 3 24 26 34 30 32 28 36

  15. Homework worksheet .5000 4 also fine: 50% .5000 z = 0 24 26 34 30 32 28 36

  16. Homework worksheet Go to table 33-30 z = 1.5 z = .4332 2 5 also fine: 43.32% .4332 z = 1.5 24 26 34 30 32 28 36

  17. Go to table Add area Lower half 33-30 z = 1.5 z = .4332 .4332 + .5000 = .9332 2 6 also fine: 93.32% .9332 .4332 .5000 z = 1.5 24 26 34 30 32 28 36

  18. Homework worksheet Subtract from .5000 Go to table 33-30 z = .4332 = 1.5 .5000 - .4332 = .0668 2 7 also fine: 6.68% .4332 .0668 z = 1.5 24 26 34 30 32 28 36

  19. Go to table Add to upper Half of curve 29-30 = -.5 z = .1915 .5000 + .1915 = .6915 2 8 also fine: 69.15% .6915 .1915 .5000 z = -.5 24 26 34 30 32 28 36

  20. 25-30 = = -2.5 .4938 2 Go to table .4938 + .1915 = .6853 31-30 .1915 =.5 = Go to table 2 9 also fine: 68.53% .6853 .1915 .4938 z =-2.5 z = .5 24 26 34 30 32 28 36

  21. Subtract From .5000 Go to table 27-30 z = .4332 = -1.5 .5000 - .4332 = .0668 2 10 also fine: 6.68% .5000 .0668 .4332 z =-1.5 24 26 34 30 32 28 36

  22. Add lower Half of curve Go to table 25-30 = -2.5 z = .4938 .5000 + .4938 = .9938 2 11 also fine: 99.38% .9938 .5000 .4938 z =-2.5 24 26 34 30 32 28 36

  23. Subtract from .5000 Go to table 32-30 z = .3413 = 1.0 .5000 - .3413 = .1587 2 12 also fine: 15.87% .3413 .1587 .5000 z =1 24 26 34 30 32 28 36

  24. 50th percentile = median 30 13 In a normal curve Median= Mean = Mode z =0 24 26 34 30 32 28 36

  25. 28 32 14 .6800 1 sd 1 sd z =-1 z = 1 24 26 34 30 32 28 36

  26. Find area of interest 77th percentile .7700 - .5000 = .2700 Find nearest z = .74 15 x = mean + z σ = 30 + (.74)(2) = 31.48 z table provides area from mean to score .5000 .2700 .7700 z =.74 ? 24 31.48 30 36

  27. Find area of interest 13th percentile Find nearest z = -1.13 .5000 - .1300 = .3700 16 x = mean + z σ = 30 + (-1.13)(2) = 27.74 Note: .13 +.37 =.50 z table provides area from mean to score .3700 .1300 z =-1.13 ? 27.74 24 30 36

  28. Please use the following distribution with a mean of 200 and a standard deviation of 40. 80 120 280 200 240 160 320

  29. .6800 17 also fine: 68.00% also fine: .6826 .6800 1 sd 1 sd z =-1 z = 1 200 240 160

  30. .9500 18 also fine: 95.00% also fine: .9544 .9500 2 sd 2 sd z =-2 z = 2 120 280 200

  31. .9970 19 also fine: 99.70% also fine: .9974 .9970 3 sd 3 sd z =-3 z = 3 80 200 320

  32. Go to table 230-200 = .75 = .2734 20 40 also fine: 27.34% .2734 z =.75 80 120 280 200 240 160 320

  33. Go to table Add to upper Half of curve 180-200 = -.5 .5000 + .1915 = .6915 z = .1915 22 40 also fine: 69.15% .6915 .1915 .5000 z =-.5 80 120 280 200 240 160 320

  34. Subtract from .5000 Go to table 236-200 .5000 - .3159 = .1841 .3159 = 0.9 z = 40 23 also fine: 18.41% .3159 .1841 z =.9 80 120 280 200 240 160 320

  35. 192 - 200 z = = -.2 .0793 40 Go to table .0793 + .2088 = .2881 222 - 200 z = .2088 =.55 24 Go to table 40 also fine: 28.81% .2881 .2088 .0793 z =-.2 z =.55 80 120 280 200 240 160 320

  36. .4693 + .5000 = .9693 Add area Lower half Go to table 275-200 .4693 or .4699 = 1.875 z = .4699 + .5000 = .9699 40 25 Please note: If z-score rounded to 1.88, then percentile = 96.99% also fine: 96.93% .9693 .4693 .5000 z =1.875 80 120 280 200 240 160 320

  37. .5000 - .4911 = .0089 Add area Lower half Go to table 295-200 .4911 or .4913 z = 2.375 z = 40 .5000 - .4913 = .0087 26 Please note: If z-score rounded to 2.38, then area = .0087 also fine: 0.89% .4911 .0089 z =2.375 80 120 280 200 240 160 320

  38. Go to table Add to upper Half of curve 130-200 = -1.75 .5000 + .4599 = .9599 z = .4599 27 40 also fine: 95.99% .9599 .5000 .4599 z =-1.75 80 120 280 200 240 160 320

  39. Go to table 130-200 Subtract from .5000 = -1.75 .5000 - .4599 = .0401 z = .4599 40 28 also fine: 4.01% .5000 .4599 .0401 z =-1.75 80 120 280 200 240 160 320

  40. Find area of interest 99th percentile Find nearest z = 2.33 .9900 - .5000 = .4900 29 x = mean + z σ = 200 + (2.33)(40) = 293.2 z table provides area from mean to score .5000 .4900 .9900 z =2.33 ? 293.2 80 120 200 240 160

  41. Find area of interest 33rd percentile Find nearest z = .44 .5000 - .3300 = .1700 30 x = mean + z σ = 200 + (-.44)(40) = 182.4 Note: .33 +.17 =.50 z table provides area from mean to score .1700 .3300 z =-.44 ? 182.4 80 280 200 240 320

  42. Find area of interest 40th percentile Find nearest z = -.25 .5000 - .4000 = .1000 31 x = mean + z σ = 200 + (-.25)(40) = 190 Note: .40 +.10 =.50 z table provides area from mean to score .1000 .4000 z =-.25 ? 182.4 80 280 200 240 320

  43. Find area of interest 67th percentile Find nearest z = .44 .6700 - .5000 = .1700 32 x = mean + z σ = 200 + (.44)(40) = 217.6 z table provides area from mean to score .1700 z =.44 80 ? 217.6 200 320

  44. . Find score associated with the 75th percentile 75th percentile Go to table nearest z = .67 .2500 x = mean + z σ = 30 + (.67)(2) = 31.34 .7500 .25 .5000 24 36 ? 28 34 26 30 31.34 Additional practice z = .67

  45. . Find the score associated with the 25th percentile 25th percentile Go to table nearest z = -.67 .2500 x = mean + z σ = 30 + (-.67)(2) = 28.66 .2500 .25 .25 28.66 24 ? 36 28 34 26 30 Additional practice z = -.67

  46. . Try this one: Please find the (2) raw scores that border exactly the middle 95% of the curve Mean of 30 and standard deviation of 2 Go to table .4750 nearest z = 1.96 mean + z σ = 30 + (1.96)(2) = 33.92 Go to table .4750 nearest z = -1.96 mean + z σ = 30 + (-1.96)(2) = 26.08 .9500 .475 .475 Additional practice 26.08 33.92 ? ? 24 32 36 28 30

  47. . Try this one: Please find the (2) raw scores that border exactly the middle 95% of the curve Mean of 100 and standard deviation of 5 Go to table .4750 nearest z = 1.96 mean + z σ = 100 + (1.96)(5) = 109.80 Go to table .4750 nearest z = -1.96 mean + z σ = 100 + (-1.96)(5) = 90.20 .9500 .475 .475 Additional practice 90.2 109.8 ? ? 85 105 115 95 100

  48. . Try this one: Please find the (2) raw scores that border exactly the middle 99% of the curve Mean of 30 and standard deviation of 2 Go to table .4750 nearest z = 1.96 mean + z σ = 30 + (2.58)(2) = 35.16 Go to table .4750 nearest z = -1.96 mean + z σ = 30 + (-2.58)(2) = 24.84 .9900 .495 .495 Additional practice 24.84 35.16 ? ? 32 28 30

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