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Lecturer’s desk

Screen. Cabinet. Cabinet. Lecturer’s desk. Table. Computer Storage Cabinet. Row A. 3. 4. 5. 19. 6. 18. 7. 17. 16. 8. 15. 9. 10. 11. 14. 13. 12. Row B. 1. 2. 3. 4. 23. 5. 6. 22. 21. 7. 20. 8. 9. 10. 19. 11. 18. 16. 15. 13. 12. 17. 14. Row C. 1. 2.

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Lecturer’s desk

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  1. Screen Cabinet Cabinet Lecturer’s desk Table Computer Storage Cabinet Row A 3 4 5 19 6 18 7 17 16 8 15 9 10 11 14 13 12 Row B 1 2 3 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row C 1 2 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row D 1 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row E 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row F 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 Row G 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 29 10 19 11 18 16 15 13 12 17 14 28 Row H 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row I 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 1 Row J 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 27 1 Row K 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row L 20 1 19 2 18 3 17 4 16 5 15 6 7 14 13 INTEGRATED LEARNING CENTER ILC 120 9 8 10 12 11 broken desk

  2. 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

  3. Homework due – Wednesday (October 9th) On class website: Please print and complete homework worksheet #11 Calculating z-score, raw scores and areas under normal curve Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  4. Use this as your study guide By the end of lecture today10/7/13 Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Percentiles

  5. Schedule of readings Before next exam (October 18th) Please read chapters 5, 6, & 8 in Ha & Ha 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

  6. Lab sessions Labs continue this week with Project 1

  7. One positive correlation One negative correlation One t-test

  8. Raw scores, z scores & probabilities The normal curve is defined mostly by its mean, and standard deviation. Once we know that we can figure out a lot z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) Given any of these values (raw score, area, z score) and you can figure out the other two.

  9. z scores – Remember from last class 1. In this formula, what does this symbol refer to? The standard deviation (population) sigma • What is it called? • What does it mean? • Is it a parameter or statistic? parameter 2. In this formula, what does this symbol refer to? The mean (population) mu • What is it called? • What does it mean? • Is it a parameter or statistic? parameter The mean (sample) 3. In this formula, what does this symbol refer to? x-bar • What is it called? • What does it mean? • Is it a parameter or statistic? statistic 4. In this formula, what does this symbol refer to? The standard deviation (sample) s • What is it called? • What does it mean? • Is it a parameter or statistic? statistic Raw score that you are changing into a z-score The number of standard deviations you are from the mean 5. In this formula, what does this symbol refer to? 6. What is a z score?

  10. Mean = 100 Standard deviation = 5 If we go up one standard deviation z score = +1.0 and raw score = 105 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 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 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

  11. Raw scores, z scores & probabilities Distance from the mean (z scores) convert convert Proportion of curve (area from mean) Raw Scores (actual data) 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” Proportion of curve (area from mean) Raw Scores (actual data) Distance from the mean (z scores) convert convert

  12. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table • probability • proportion • percent • area under the curve 68% 34% 34%

  13. Scores, standard deviations, and probabilities Actually 68.26 Actually 95.44 To be exactly 95% we will use z = 1.96

  14. Scores, standard deviations, and probabilities What is total percent under curve? What proportion of curve is above the mean? 100% .50 mean = 260 standard deviation = 20 200 220 240 260 280 300 320 • µ • σ Given any of these values (score, probability of occurrence, or distance from the mean) and you can figure out the other two.

  15. Scores, standard deviations, and probabilities What score is associated with 50th percentile? What percent of curve is below a score of 260? 50% median 260 200 220 240 260 280 300 320 • µ • σ mean = 260 standard deviation = 20

  16. 50 60 68% Mean = 50sd = 10 We’re going to want to talk probabilities (area under the curve) for pairs of scores 34% 34% Find the area under the curve that falls between 50 and 60 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 1) Draw the picture 2) Find z score z score = raw score - mean standard deviation 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  17. 50 60 1) Draw the picture 2) Find z score 34.13% 3) Go to z table - find area under correct column 4) Report the area z = 1 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 50 60 10

  18. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table... • probability • proportion • percent • area under the curve 68% 34% 34%

  19. z table z table Mean = 50 Standard deviation = 10 68.26% Find the area under the curve that falls between 40 and 60 34.13% 34.13% z score = raw score - mean standard deviation Hint always draw a picture! z score = 60 - 50 10 z score = 40 - 50 10 z score = 10 = 1.0 10 z score = 10 = -1.0 10 z score of 1 = area of .3413 z score of 1 = area of .3413 .3413 + .3413 = .6826

  20. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table • probability • proportion • percent • area under the curve 68% 34% 34%

  21. Mean = 50 Standard deviation = 10 1) Draw the picture 2) Find z score 3) Go to z table - find area under correct column 4) Report the area Find the area under the curve that falls between 30 and 50 z-table (from z to area) Distance from the mean ( from raw to z scores) z score = raw score - mean standard deviation Raw Scores (actual data) Proportion of curve (area from mean) z score = 30 - 50 10 z score = - 20 = - 2.0 10 Hint always draw a picture!

  22. z table Mean = 50 Standard deviation = 10 1) Draw the picture 2) Find z score 3) Go to z table - find area under correct column 4) Report the area 47.72% Find the area under the curve that falls between 30 and 50 z score = raw score - mean standard deviation z score = 30 - 50 10 z score = - 20 = - 2.0 10 z score of - 2 = area of .4772 Hint always draw a picture! Hint always draw a picture!

  23. Let’s do some problems z table Mean = 50 Standard deviation = 10 47.72% Find the area under the curve that falls between 70 and 50 z score = raw score - mean standard deviation z score = 70 - 50 10 z score = 20 = +2.0 10 z score of 2 = area of .4772 Hint always draw a picture!

  24. Let’s do some problems Mean = 50 Standard deviation = 10 .4772 .4772 95.44% z score of 2 = area of .4772 z-table (from z to area) Distance from the mean ( from raw to z scores) Find the area under the curve that falls between 30 and 70 Raw Scores (actual data) Proportion of curve (area from mean) .4772 + .4772 = .9544 Hint always draw a picture!

  25. Scores, standard deviations, and probabilities Actually 68.26 Actually 95.44 To be exactly 95% we will use z = 1.96

  26. Let’s do some problems ? Mean = 50Standard deviation = 10 60 Find the area under the curve that falls below 60 means the same thing as Find the percentile rank for score of 60

  27. Let’s do some problems ? 60 Mean = 50Standard deviation = 10 Find the percentile rank for score of 60 z-table (from z to area) Distance from the mean ( from raw to z scores) .3413 .5000 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 60 - 50 10 = 1 2) Go to z table - find area under correct column (.3413) 3) Look at your picture - add .5000 to .3413 = .8413 4) Percentile rank or score of 60 = 84.13% Hint always draw a picture!

  28. ? 75 Mean = 50Standard deviation = 10 Find the percentile rank for score of 75 .4938 1) Find z score z score = 75 - 50 10 z score = 25 10 = 2.5 2) Go to z table Hint always draw a picture!

  29. ? 75 Mean = 50Standard deviation = 10 Find the percentile rank for score of 75 .4938 .5000 1) Find z score z score = 75 - 50 10 z score = 25 10 = 2.5 2) Go to z table 3) Look at your picture - add .5000 to .4938 = .9938 4) Percentile rank or score of 75 = 99.38% Hint always draw a picture!

  30. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table

  31. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 ? 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table

  32. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .3085 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table 3) Look at your picture - subtract .5000 -.1915 = .3085 4) Percentile rank or score of 45 = 30.85%

  33. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 z-table (from z to area) Distance from the mean ( from raw to z scores) 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table

  34. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 55 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table

  35. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .5 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table 3) Look at your picture - add .5000 +.1915 = .6915 4) Percentile rank or score of 55 = 69.15%

  36. Find the score for z = -2 ? Mean = 50Standard deviation = 10 30 Hint always draw a picture! Find the score that is associated with a z score of -2 z-table (from z to area) Distance from the mean ( from raw to z scores) raw score = mean + (z score)(standard deviation) Raw Scores (actual data) Proportion of curve (area from mean) Raw score = 50 + (-2)(10) Raw score = 50 + (-20) = 30 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

  37. Thank you! See you next time!!

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