2. Modern Languages 14131211109 87 6 54321 111098765 43 2 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 212019181716 1514 13 12111098 212019181716 13 12111098 141312 table 7 6 54321 Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 21 1413 Projection Booth 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 7 6 5432 1 765 43 2 1 7 6 5432 1 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 table Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 282726 2524 23 22 R/L handed broken desk Stage Lecturer’s desk Screen 1

3. MGMT 276: Statistical Inference in Management Spring 2015

4. Schedule of readings Before next exam: February 17 th Please read chapters 1 - 4 & Appendix D & E in Lind 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

5. By the end of lecture today 2/3/15 Questionnaire design and evaluation Random versus non-random sampling techniques Dot Plots Frequency Distributions - Frequency Histograms Frequency, cumulative frequency Relative frequency, cumulative relative frequency Guidelines for constructing frequency distributions

6. Homework due - (February 5 th ) Assignment 4 Describing Data Visually using MS Excel Due: Thursday, February 5 th

7. Complete this TODAY and receive extra credit! (By February 3rd 2015)

8. Questionnaire Homework There are four parts: Statement of Objectives Questionnaire itself (which is the operational definitions of the objectives) Screenshot of Excel Database Creation of 2 bar graphs representing results Must be complete and must be stapled

9. Iterative design process Peer review is an important skill in nearly all areas of business and science. Please strive to provide productive, useful and kind feedback as you complete your peer review

10. Iterative design process Please exchange questionnaires with someone near you help make the product better using peer review worksheet handed out in class You have 10 minutes You have 10 minutes

11. Review of Homework Worksheet Hand in the peer review with the questionnaire *Hand them in together*

12. Sample versus census How is a census different from a sample? Census measures each person in the specific population Sample measures a subset of the population and infers about the population – representative sample is good What’s better? Use of existing survey data U.S. Census Family size, fertility, occupation The General Social Survey Surveys sample of US citizens over 1,000 items Same questions asked each year You’ve completed constructing your questionnaire…what’s the best way to get responders??

13. Parameter – Measurement or characteristic of the population Usually unknown (only estimated) Usually represented by Greek letters (µ) Population (census) versus sample Parameter versus statistic pronounced “mu ” pronounced “mew ” Statistic – Numerical value calculated from a sample Usually represented by Roman letters (x) pronounced “x bar ”

14. Simple random sampling: each person from the population has an equal probability of being included Sample frame = how you define population Sample frame = how you define population =RANDBETWEEN(1,115) Let’s take a sample …a random sample Question: Average weight of U of A football player Sample frame population of the U of A football team Or, you can use excel to provide number for random sample Random number table – List of random numbers Random number table – List of random numbers 64 Pick 64 th name on the list (64 is just an example here) Pick 24 th name on the list

15. Systematic random sampling: A probability sampling technique that involves selecting every technique that involves selecting every kth person from a sampling frame You pick the number Other examples of systematic random sampling 1) check every 2000 th light bulb 2) survey every 10 th voter

16. Stratified sampling: sampling technique that involves dividing a sample into subgroups (or strata) and then selecting samples from each of these groups - sampling technique can maintain ratios for the different groups Average number of speeding tickets 17.7% of sample are Pre-business majors 4.6% of sample are Psychology majors 4.6% of sample are Psychology majors 2.8% of sample are Biology majors 2.8% of sample are Biology majors 2.4% of sample are Architecture majors 2.4% of sample are Architecture majors etc etc Average cost for text books for a semester 12% of sample is from California 7% of sample is from Texas 6% of sample is from Florida 6% from New York 4% from Illinois 4% from Ohio 4% from Pennsylvania 3% from Michigan etc

17. Cluster sampling: sampling technique divides a population sample into subgroups (or clusters) by region or physical space. Can either measure everyone or select samples for each cluster Textbook prices Southwest schools Southwest schools Midwest schools Midwest schools Northwest schools Northwest schools etc etc Average student income, survey by Old main area Old main area Near McClelland Around Main Gate etc Patient satisfaction for hospital 7 th floor (near maternity ward) 7 th floor (near maternity ward) 5 th floor (near physical rehab) 5 th floor (near physical rehab) 2 nd floor (near trauma center) 2 nd floor (near trauma center) etc etc

18. Snowball sampling: a non-random technique in which one or more members of a population are located and used to lead the researcher to other members of the population Used when we don’t have any other way of finding them - also vulnerable to biases Convenience sampling: sampling technique that involves sampling people nearby. A non-random sample and vulnerable to bias Judgment sampling: sampling technique that involves sampling people who an expert says would be useful. A non-random sample and vulnerable to bias Non-random sampling is vulnerable to bias

19. You’ve gathered your data…what’s the best way to display it??

20. 141720252129 162527181613 112119242011 202816131714 14168171711 11141719248 16122592017 1114161822 1418231215 1013151111 Describing Data Visually 81114171924 81214172025 91215172025 101315172025 111316172027 111316172128 111416182129 1114161822 1114161823 1114161924 Lists of numbers too hard to see patterns Organizing numbers helps Graphical representation even more clear This is a dot plot

21. Describing Data Visually 81214171924 81214172025 91315172025 101315172025 111316172027 111316172128 111416182129 1114161822 1114161823 1114161924 Measuring the “frequency of occurrence” Then figure “frequency of occurrence” for the bins We’ve got to put these data into groups (“bins”)

22. Frequency distributions Frequency distributions an organized list of observations and their frequency of occurrence How many kids are in your family? What is the most common family size?

23. Another example: How many kids in your family? 3 4 8 2 2 1 4 1 14 2 Number of kids in family 1313 1414 2424 2828 214

24. Frequency distributions Crucial guidelines for constructing frequency distributions: 1. Classes should be mutually exclusive: Each observation should be represented only once (no overlap between classes) 2. Set of classes should be exhaustive: Should include all possible data values (no data points should fall outside range) Wrong 0 - 5 5 - 10 10 - 15 Correct 0 - 4 5 - 9 10 - 14 Correct 0 - under 5 5 - under 10 10 - under 15 How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 Wrong 0 - 3 8 - 11 12 - 15 Correct 0 - 3 4 - 7 8 - 11 12 - 15 No place for our families of 4, 5, 6 or 7

25. Frequency distributions Crucial guidelines for constructing frequency distributions: 3. All classes should have equal intervals (even if the frequency for that class is zero) Wrong 0 - 1 2 - 12 14 - 15 Correct 0 - 4 5 - 9 10 - 14 Correct 0 - under 5 5 - under 10 10 - under 15 How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214

26. 4. Selecting number of classes is subjective Generally 5 -15 will often work 8 12 14 17 19 24 8 12 14 17 20 25 9 13 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 How about 6 classes? (“bins”) How about 8 classes? (“bins”) How about 16 classes? (“bins”)

27. 5. Class width should be round (easy) numbers 6. Try to avoid open ended classes For example 10 and above Greater than 100 Less than 50 Clear & Easy 8 - 11 12 - 15 16 - 19 20 - 23 24 - 27 28 - 31 8 12 14 17 19 24 8 12 14 17 20 25 9 13 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 Round numbers: 5, 10, 15, 20 etc or 3, 6, 9, 12 etc Lower boundary can be multiple of interval size Remember: This is all about helping readers understand quickly and clearly.

28. Let’s do one Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 If less than 10 groups, “ungrouped” is fine If more than 10 groups, “grouped” might be better How to figure how many values 99 - 53 + 1 = 47 Step 1: List scores 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Step 2: List scores in order Step 3: Decide whether grouped or ungrouped Step 4: Generate number and size of intervals (or size of bins) Largest number - smallest number + 1 Sample size (n) 10 – 16 17 – 32 33 – 64 65 – 128 129 - 255 256 – 511 512 – 1,024 Number of classes 5 6 7 8 9 10 11 If we have 6 bins – we’d have intervals of 8 Whaddya think? Would intervals of 5 be easier to read? Let’s just try it and see which we prefer…

29. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Scores on an exam Score Frequency 93 - 100 4 85 - 92 6 77- 84 6 69 - 76 7 61- 68 2 53 - 60 3 10 bins Interval of 5 6 bins Interval of 8 Let’s just try it and see which we prefer… Remember: This is all about helping readers understand quickly and clearly. Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1

30. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Let’s make a frequency histogram using 10 bins and bin width of 5!!

31. Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Step 6: Complete the Frequency Table Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 Relative Frequency.0715.1071.1786.1429.1071.0357.1071.0357 Relative Cumulative Frequency 1.0000.9285.8214.6428.4642.3213.2142.1785.0714.0357 6 bins Interval of 8 Just adding up the frequency data from the smallest to largest numbers Just dividing each frequency by total number to get a ratio (like a percent) Please note: 1 /28 =.0357 3/ 28 =.1071 4/28 =.1429 Just adding up the relative frequency data from the smallest to largest numbers Please note: Also just dividing cumulative frequency by total number 1/28 =.0357 2/28 =.0714 5/28 =.1786

32. http://2016.election-polls.org/President/Republican-Primary/?political_poll=1058 Who is your favorite candidate Candidate Frequency Mitt Romney84 Jeb Bush68 Dr. Ben Carson 60 Scott Walker44 Ted Cruz36 Mike Huckabee36 Chris Christy28 Undecided20 Rand Paul16 Rick Perry 8 Homework Preview Simple Frequency Table – Qualitative Data We asked 400 Republicans “Who is your favorite candidate?” Relative Frequency.2100.1700.1500.1100.0900.0700.0500.0400.0200 Just divide each frequency by total number Please note: 80 /400 =.2100 68 /400 =.1700 60 /.400 =.1500 Percent 21% 17% 15% 11% 9% 7% 5% 4% 2% If one million Republicans voted today how many would vote for each candidate? Number expected to vote 210,000 170,000 150,000 110,000 90,000 70,000 50,000 40,000 20,000 Just multiply each relative frequency by 100 Please note:.2100 x 100 = 21%.1700 x 100 = 17%.1500 x 100 = 15% Just multiply each relative frequency by one million Please note:.2100 x million = 210,000.1700 x million = 170,000.1500 x million = 150,000 Data from January 30 th 2015

33. Describing Data Visually 81214171924 81214172025 91315172025 101315172025 111316172027 111316172128 111416182129 1114161822 1114161823 1114161924 Measuring the “frequency of occurrence”

34. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Remember Dot Plots Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1 Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 5: Generate frequency histogram

35. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1 Remember Dot Plots Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 5: Generate frequency histogram

36. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1 Remember Dot Plots Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 5: Generate frequency histogram

37. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1 Remember Dot Plots Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 5: Generate frequency histogram

38. Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Step 5: Generate frequency histogram Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1

39. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 Scores on an exam Score Frequency 95 - 992 90 - 94 3 85 - 89 5 80 – 845 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 6 5 4 3 2 1 Generate frequency polygon Plot midpoint of histogram intervals Connect the midpoints

40. Scores on an exam 82586480 75728773 88948478 93697060 53847687 84618995 87917599 Scores on an exam Score 95 – 99 90 - 94 85 - 89 80 – 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 Score on exam 80 - 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 90 - 94 95 - 99 85 - 89 30 25 20 15 10 5 Frequency ogive is used for cumulative data Generate frequency ogive (“oh-jive”) Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 Connect the midpoints Plot midpoint of histogram intervals

41. Pareto Chart: Categories are displayed in descending order of frequency

42. Stacked Bar Chart: Bar Height is the sum of several subtotals

43. Simple Line Charts: Often used for time series data (continuous data) (the space between data points implies a continuous flow) Note: Can use a two-scale chart with caution Note: Fewer grid lines can be more effective Note: For multiple variables lines can be better than bar graph

44. Pie Charts: General idea of data that must sum to a total (these are problematic and overly used – use with much caution) Bar Charts can often be more effective Exploded 3-D pie charts look cool but a simple 2-D chart may be more clear Exploded 3-D pie charts look cool but a simple 2-D chart may be more clear

45. Data based on Gallup poll on 8/24/11 Who is your favorite candidate Candidate Frequency Rick Perry29 Mitt Romney17 Ron Paul13 Michelle Bachman10 Herman Cain 4 Newt Gingrich 4 No preference23 Simple Frequency Table – Qualitative Data We asked 100 Republicans “Who is your favorite candidate?” Relative Frequency.2900.1700.1300.1000.0400.2300 Just divide each frequency by total number Please note: 29 /100 =.2900 17 /100 =.1700 13 /100 =.1300 4 /100 =.0400 Percent 29% 17% 13% 10% 4% 23% If 22 million Republicans voted today how many would vote for each candidate? Number expected to vote 6,380,000 3,740,000 2,860,000 2,200,000 880,000 5,060,000 Just multiply each relative frequency by 100 Please note:.2900 x 100 = 29%.1700 x 100 = 17%.1300 x 100 = 13%.0400 x 100 = 4% Just multiply each relative frequency by 22 million Please note:.2900 x 22m = 6,667k.1700 x 22m = 3,740k.1300 x 22m = 2,860k.0400 x 22m= 880k