1 / 78

Please start your Daily Portfolio

. Please start your Daily Portfolio.

gwylan
Download Presentation

Please start your Daily Portfolio

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. . Please start your Daily Portfolio

  2. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Summer Session II, 20139:00 - 11:20am Monday - FridayRoom 312 Social Sciences (Monday – Thursdays)Room 480 Marshall Building (Fridays) Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

  3. Please click in Study Guide is online My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please double check All cell phones other electronic devices are turned off and stowed away

  4. Homework due – Wednesday (July 17th) On class website: Please print and complete homework worksheet #6 Calculating z-scores, raw scores and probabilities

  5. Schedule of readings Before Friday (July 19th) Please read chapters 3, 4, 5, & 6 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. Remember… In a negatively skewed distribution: mean < median < mode 88 = mode = tallest point 86 = median = middle score 84 = mean = balance point Note: Always “frequency” Note: Label and Numbers

  7. Use this as your study guide By the end of lecture today7/16/13 Objectives in Research Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Percentiles Empirical, classical and subjective approaches Probability of an event Complement of an event; Union of two events Intersection of two events; Mutually exclusive events Collectively exhaustive events Conditional probability Probability of an event

  8. Class standing 4 Ordinal # Bags Sold Quasi # of bags of peanuts sold Ratio Between One-way ANOVA Fr So JrSr Class Standing

  9. Homework Review Average # of bags of peanuts sold Frequency 95% Confidence Interval Average # of bags of peanuts sold

  10. Homework Review Type of Diet 2 Nominal Weight Loss True Experiment Weight Loss Ratio Between Regular New T-test Type of Diet

  11. Homework Review Type of Diet Male 2 Gender Weight Loss 2 Female Mixed Weight Loss Regular New Between Type of Diet Two-way ANOVA

  12. Homework Review Distance Time Strong, positive +1.0 Correlation Time Distance

  13. Why do we concern ourselves about research? – Five objectives 1. To explore potential phenomena • explore whether phenomenon is present • explore a phenomenon with a fresh take • generate new ideas and discover relationships

  14. Why do we concern ourselves about research? – Five objectives 1. To explore potential phenomena • explore whether phenomenon is present • explore a phenomenon with a fresh take • generate new ideas and discover relationships Yo, you wanna meet up, have a seizure whilst listening to the noise of a wampwampwampwamp wampwampwampwampwampuntil your ears bleed?"

  15. Why do we concern ourselves about research in business? – Five objectives 2. To describe phenomena • build a vocabulary of constructs and make distinctions between similar constructs • (how is dubstep different from techno or house?) • cluster similar characteristics into related constructs . - Types of management style - Strategies for quality control

  16. Why do we concern ourselves about research in business? – Five objectives 3. To explain and model phenomena • explanation: find cause and effect relationships • propose mechanisms that determine outcomes • show how and why a phenomenon operates as it does

  17. Why do we concern ourselves about research in business? – Five objectives 4. To predict future behavior • what characteristics are likely to result in workerproductivity, consumer behavior, etc... • explanations can help with predictions, but being able to predict an outcome doesn’t necessarily provide a good explanation

  18. Why do we concern ourselves about research in business? – Five objectives 5. To influence behavior • how can we use what we know about human behavior to affect how people around us react and behave (and do what we want) • increasing probability of sales • supervisors increasing probability of happy employees • parent increasing probability of child taking out the trash • to advance better practices

  19. 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.

  20. 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7% 68% Confidence interval 95% Confidence interval 99% Confidence interval You already know this by heart

  21. Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 z = -1 Mean = 50 S = 10 (Note S = standard deviation) 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

  22. Raw scores, z scores & probabilities 2 sd above and below mean 95% z = -2 z = +2 Mean = 50 S = 10 (Note S = standard deviation) 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

  23. Raw scores, z scores & probabilities 3 sd above and below mean 99.7% z = +3 z = -3 Mean = 50 S = 10 (Note S = standard deviation) 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

  24. z scores 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

  25. Find z score for raw score of 60 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 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 z = 1 10 Mean = 50 S = 10 (Note S = standard deviation)

  26. Find z score for raw score of 30 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 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 30 z = - 2 10 Mean = 50 S = 10 (Note S = standard deviation)

  27. Find z score for raw score of 70 Raw scores, z scores & probabilities z-table (from z to area) Distance from the mean ( from raw to z scores) If we go up to score of 70 we are going up 2.0 standard deviations Raw Scores (actual data) Proportion of curve (area from mean) Then, z score = +2.0 z score = raw score - mean standard deviation z score = 70 – 50 . 10 = 20. 10 = 2 Mean = 50 S = 10 (Note S = standard deviation)

  28. Find z score for raw score of 80 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 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 80 z = 3 10 Mean = 50 S = 10 (Note S = standard deviation)

  29. Find z score for raw score of 20 Raw scores, z scores & probabilities z-table (from z to area) Distance from the mean ( from raw to z scores) If we go down to score of 20 we are going down 3.0 standard deviations Raw Scores (actual data) Proportion of curve (area from mean) Then, z score = -3.0 z score = raw score - mean standard deviation z score = 20 – 50 10 = - 30 . 10 = - 3 Mean = 50 S = 10 (Note S = standard deviation)

  30. z scores - Writing Assignment 1. In this formula, what does this symbol refer to? 2. In this formula, what does this symbol refer to? 3. In this formula, what does this symbol refer to? 4. In this formula, what does this symbol refer to? 5. In this formula, what does this symbol refer to? 6. What is a z score?

  31. z scores - Writing Assignment 1. In this formula, what does this symbol refer to? The standard deviation (population) 2. In this formula, what does this symbol refer to? The mean (population) 3. In this formula, what does this symbol refer to? Raw score that you are changing into a z-score 4. In this formula, what does this symbol refer to? The mean (sample) 5. In this formula, what does this symbol refer to? The standard deviation (sample) 6. What is a z score? The number of standard deviations you are from the mean

  32. 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

  33. 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

  34. 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%

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

  36. Scores, standard deviations, and probabilities What is total percent under curve? What proportion of curve is above the mean? .50 100% Given any of these values (score, probability of occurrence, or distance from the mean) and you can figure out the other two.

  37. Scores, standard deviations, and probabilities What score is associated with 50th percentile? What percent of curve is below a score of 50? 50% mean Mean = 50 S = 10 (Note S = standard deviation)

  38. 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!

  39. 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

  40. 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%

  41. 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 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) z score = raw score - mean standard deviation Raw Scores (actual data) Proportion of curve (area from mean) z score = 60 - 50 10 z score = 10 = 1.0 10 z score of 1 = area of .3413 Hint always draw a picture!

  42. 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

  43. 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%

  44. 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!

  45. 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!

  46. 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!

  47. 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!

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

More Related