Introduction to Statistics for the Social Sciences

1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall, 2014Room 120 Integrated Learning Center (ILC)10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

2. Preview of Questionnaire Homework • There are four parts: • Statement of Objectives • Questionnaire itself (which is the operational definitions of the objectives) • Data collection and creation of database • Creation of graphs representing results Hand in questionnaire project (Homework assignments 3 & 4)

3. Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs next week • Remember: • Bring electronic copy of your data (flash drive or email it to yourself) • Your data should have correct formatting • See Lab Materials link on class website to double-check formatting of excel is exactly consistent

4. Schedule of readings Before next exam (September 26th) 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

5. A noteon doodling Reminder

6. Use this as your study guide By the end of lecture today9/12/14 • Dot Plots • Frequency Distributions - Frequency Histograms • Frequency, relative frequency • Guidelines for constructing frequency distributions • Correlational methodology • Positive, Negative and Zero correlation

7. Homework due – Monday (September 15th) On class website: please print and complete homework worksheet #5

8. Descriptive vs inferential statistics Sample versus population Descriptive statistics - organizing and summarizing data Inferential statistics - generalizing beyond actual observations making “inferences” based on data collected

9. Descriptive or inferential? Descriptive statistics - organizing and summarizing data Inferential statistics - generalizing beyond actual observations making “inferences” based on data collected What is the average height of the basketball team? Measured all of the players and reported the average height Measured only a sample of the players and reported the average height for team In this class, percentage of students who support the death penalty? Measured all of the students in class and reported percentage who said “yes” Measured only a sample of the students in class and reported percentage who said “yes” Based on the data collected from the students in this class we can conclude that 60% of the students at this university support the death penalty Measured all of the students in class and reported percentage who said “yes”

10. Descriptive or inferential? Descriptive statistics - organizing and summarizing data Inferential statistics - generalizing beyond actual observations making “inferences” based on data collected Men are in general taller than women Measured all of the citizens of Arizona and reported heights Shoe size is not a good predictor of intelligence Measured all of the shoe sizes and IQ of students of 20 universities Blondes have more fun Asked 500 actresses to complete a happiness survey The average age of students at the U of A is 21 Asked all students in the fraternities and sororities their age

11. Descriptive vs inferential statistics Descriptive statistics - organizing and summarizing data Inferential statistics - generalizing beyond actual observations making “inferences” based on data collected To determine this we have to consider the methodologies used in collecting the data

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

13. Describing Data Visually Lists of numbers too hard to see patterns 14 17 20 25 21 29 16 25 27 18 16 13 11 21 19 24 20 11 20 28 16 13 17 14 14 16 8 17 17 11 11 14 17 19 24 8 16 12 25 9 20 17 11 14 16 18 22 14 18 23 12 15 10 13 15 11 11 8 11 14 17 19 24 8 12 14 17 20 25 9 12 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 Organizing numbers helps Graphical representation even more clear This is a dot plot

14. Describing Data Visually 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 Measuring the “frequency of occurrence” Then figure “frequency of occurrence” for the bins We’ve got to put these data into groups (“bins”)

15. 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?

16. Another example: How many kids in your family? Number of kids in family 1 3 1 4 2 4 2 8 2 14 14 4 2 1 4 2 3 2 1 8

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

18. Frequency distributions Number of kids in family 1 3 1 4 2 4 2 8 2 14 How many kids are in your family? What is the most common family size? Crucial guidelines for constructing frequency distributions: 3. All classes should have equal intervals (even if the frequency for that class is zero) Correct 0 - 4 5 - 9 10 - 14 Wrong 0 - 1 2 - 12 14 - 15 Correct 0 - under 5 5 - under 10 10 - under 15

19. 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 4. Selecting number of classes is subjective Generally 5 -15 will often work How about 6 classes? (“bins”) How about 16 classes? (“bins”) How about 8 classes? (“bins”)

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

21. Let’s do one 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 53 58 60 61 64 69 70 72 73 75 75 76 78 80 82 84 84 84 87 87 87 88 89 91 93 94 95 99 Step 1: List scores Step 2: List scores in order Step 3: Decide whether grouped or ungrouped If less than 10 groups, “ungrouped” is fine If more than 10 groups, “grouped” might be better How to figure how many values Largest number - smallest number + 1 99 - 53 + 1 = 47 Step 4: Generate number and size of intervals (or size of bins) If we have 6 bins – we’d have intervals of 8 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 Let’s just try it and see which we prefer… Whaddya think? Would intervals of 5 be easier to read?

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

23. 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 Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 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!!

24. 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 Step 6: Complete the Frequency Table Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 RelativeCumulative Frequency 1.0000 .9285 .8214 .6428 .4642 .3213 .2142 .1785 .0714 .0357 Relative Frequency .0715 .1071 .1786 .1786 .1429 .1071 .0357 .1071 .0357 .0357 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 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 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

25. 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 Where are we? Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Relative Frequency .0715 .1071 .1786 .1786 .1429 .1071 .0357 .1071 .0357 .0357 Cumulative Rel. Freq. 1.0000 .9285 .8214 .6428 .4642 .3213 .2142 .1785 .0714 .0357 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 Cumulative Frequency Data Cumulative Frequency Histogram

26. 55 - 59 75 - 79 50 - 54 60 - 64 80 - 84 95 - 99 70 - 74 85 - 89 65 - 69 90 - 94 Score on exam 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 Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 5: Generate frequency histogram Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 6 5 4 3 2 1

27. 55 - 59 75 - 79 50 - 54 60 - 64 80 - 84 95 - 99 70 - 74 85 - 89 65 - 69 90 - 94 Score on exam 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 Generate frequency polygon Plot midpoint of histogram intervals Connect the midpoints Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 6 5 4 3 2 1

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

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

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

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

32. Pie Charts: General idea of data that must sum to a total(these are problematic and overly used – use with much caution) 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 Bar Charts can often be more effective

33. Simple Frequency Table – Qualitative Data We asked 100 Republicans “Who is your favorite candidate?” Number expected to vote 6,380,000 3,740,000 2,860,000 2,200,000 880,000 880,000 5,060,000 Who is your favorite candidate Candidate Frequency Rick Perry 29 Mitt Romney 17 Ron Paul 13 Michelle Bachman 10 Herman Cain 4 Newt Gingrich 4 No preference 23 Relative Frequency .2900 .1700 .1300 .1000 .0400 .0400 .2300 Percent 29% 17% 13% 10% 4% 4% 23% If 22 million Republicans voted today how many would vote for each candidate? Just divide each frequency by total number Just multiply each relative frequency by 22 million Just multiply each relative frequency by 100 Please note: 29 /100 = .2900 17 /100 = .1700 13 /100 = .1300 4 /100 = .0400 Please note: .2900 x 22m = 6,667k .1700 x 22m = 3,740k .1300 x 22m = 2,860k .0400 x 22m= 880k Please note: .2900 x 100 = 29% .1700 x 100 = 17% .1300 x 100 = 13% .0400 x 100 = 4% Data based on Gallup poll on 8/24/11

37. Designed our study / observation / questionnaire Collected our data Organize and present our results

38. Scatterplot displays relationships between two continuous variables Correlation: Measure of how two variables co-occur and also can be used for prediction Range between -1 and +1 The closer to zero the weaker the relationship and the worse the prediction Positive or negative

39. Correlation Range between -1 and +1 +1.00 perfect relationship = perfect predictor +0.80 strong relationship = good predictor +0.20 weak relationship = poor predictor 0 no relationship = very poor predictor -0.20 weak relationship = poor predictor -0.80 strong relationship = good predictor -1.00 perfect relationship = perfect predictor

40. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Height of Mothers by Height of Daughters Height ofMothers Positive Correlation Height of Daughters

41. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Brushing teeth by number cavities BrushingTeeth Negative Correlation NumberCavities

42. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other Height in inches and height in feet Speed (mph) and time to finish race Positive correlation Negative correlation

43. Correlation The more closely the dots approximate a straight line,(the less spread out they are) the stronger the relationship is. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other No variability in the scatterplot The dots approximate a straight line

44. Correlation

45. Thank you! See you next time!!