1. http://faculty.wwu.edu/~donovat/ps366/

2. Review Chapter 2, p. 56 – SPSS MARITAL – How would you describe where most students in the sample were raised? – What percent of the sample is divorced? – What percent of the sample is married? – What percent would you describe as currently being single?

3. Chapter 5 Homework # 7, p. 171-72 (in slides last week) #9 p. 172-73 #12 p. 174-75

4. Projects 1) Perceptions of Western Washington Univ. 2) Presidential campaign – Which candidates mobilize? 3) Opinion on national issues – Which issues of greatest concern?, Why? Guns, Immigration, House GOP, etc.

5. Review Friday’s Lab How do we measure a country’s level of development? – Define the concept

6. Review Friday’s Lab How do we measure a country’s level of development? Some measures: – Human Development Index – GDP – ??

8. Describe the graph – Range, standard deviation – Mean, median, mode Which country at center of distribution? Which countries at the extremes?

9. GDP

10. HDI vs GDP What differences? Median countries? Shape of distribution Correlated at.79

12. Friday, review 3 rd factor that measures ‘development’ Discuss: which measure is best / most valid? Why?

13. Chapter 6: Normal Distribution Normal curve – Theoretical, not an empirical distribution – Mean = median = mode – Constant proportions of area under normal curve – Standard deviation = fixed relationship between distance from mean and area under the curve

14. Std Dev & Normal Curve

18. Normal Curve and z-scores Difference between and observation and the mean can be expressed in standard scores Z scores

19. Normal curve and z scores Calculate z-score observed score - mean Z =_____________________ Standard deviation

20. Normal curve and z scores Calculate z-score Y – Y “Hat” Z =_____________________ Standard deviation

21. Z scores & normal distribution Where is a country with an HDI of.75? – mean =.696 – sd =.186 – Z = (.75-.696 ) /.186 =.06/.186 =.32 – 0.32 deviations beyond the mean

22. Z scores & normal distribution What is the raw score for a country with a z score of 1.5 on HDI – Y = Y“hat” + Z(std dev.) – Y=.696 + (1.5*.186) =.696 +.279 =.975 – so, a country with HDI at.975 = 1.5 standard deviations beyond the mean

23. Standard Normal Distribution Appendix B in text, p. 480

24. Z scores & Normal curve Standard normal distribution – Normal distribution represented by z scores

25. Normal curve and z scores Example: What proportion of countries would we expect to find between the mean and 1.45 std dev. (if normal distribution?) What proportion below the mean? What proportion between mean and Z = +1.45

26. http://www.mathsisfun.com/data/standard- normal-distribution-table.html http://www.mathsisfun.com/data/standard- normal-distribution-table.html

27. Normal curve and z-scores 1,200 students in stats class, 1983-1993 Mean 70.07 Median 70 Mode70 Std. deviation 10.27

28. Translate scores into Zs Score of 40: (40-70.07)/10.27 =-2.93 Score of 70: (70-70.07) /10.27 =-0.01 Score of 90: (90-70.07) / 10.27 = 1.94

29. Z scores & normal distribution What % of students scored above 90? – Z for 90 is 1.94 – Use standard normal table (p. 480)

30. B C.500 of total area -Z MEAN + Z = 1.94

31. B C.500 of total area -Z MEAN + Z = 1.94 70 90 Check table to determine area of B; or area of C

32. .4738.0262.500 of total area -Z MEAN + Z = 1.94 70 90 Check table to determine area of B

33. .4738. 0262.500 of total area -Z MEAN + Z = 1.94 70 90.50 +.4738 =.9738. 97.38% scored lower than 90

34. .4738. 0262.500 of total area -Z MEAN + Z = 1.94 70 90.50 +.4738 =.9738. 2.62% scored higher than 90

35. Translate scores into Zs Score of 40: (40-70.07)/10.27 =-2.93 Score of 70: (70-70.07) /10.27 =-0.01 Score of 90: (90-70.07) / 10.27 = 1.94

36. Z score and normal curve What percent scored below 40 on the stats exam? – Z for 40 = -2.93 – use standard normal table

37. B C.500 of total area -Z MEAN + Z 40 70

38. B:.4983 C: 0.0017.500 of total area -Z MEAN + Z 40 70 Area C = 0.0017 of area; Area B =.4983 0.17% scored lower than 40

39. Z scores and normal curve Standard Normal Table expressed in proportions Easily translated into percentages – multiply by 100 Easily translated into percentiles

40. Z scores and normal curve Find the percentile rank of a score of 85: – Z = (score-mean) / std. deviation – Z = (85-70.07) / 10.27 = 1.45 Find the percentile rank of a score of 90 – Z = (score-mean) / std. deviation – Z = (90-70.07) / 10.27 = 1.94

41. . 0262, or 2.62%.500 +.4738 of total area = 97.38% -Z MEAN + Z = 1.94 70 90 Score of 90 higher than 97.38% who took stats test 97.38 th percentile B C

42. . 0735, or 7.35%.500 +.4265 of total area = 92.65% -Z MEAN + Z = 1.45 70 85 Score of 80 higher than 92.65% who took stats test 92.65 th percentile B C

43. Normal curve: percentiles OK, a score of 70 (mean = 70.07) – Z = ?? A score of 60 (below the mean, sd = 10.27) – Z = ?? positive or negative guess

44. Normal curve: percentiles A score of 70 – Z = -0.01 A score of 60 (below the mean) – Z = (score – mean) / st dev. (60-70.07) / 10.27 = - 0.98

45. . Z = -0.98 MEAN + Z 60 70 Score of 60 higher than 16.35% who took stats test 16.35 th percentile B:.3365; 33.65% C:.1635, 16.35%

46. Percentiles Range from 0 to 100 Percent of observations above a point Example – SAT math score in 82nd percentile – SAT writing score in 88th percentile – SAT vocabulary score in 75th percentile

47. Percentiles SAT scores – mean 500 – st dev 100 What % score above 625?

48. Percentiles SAT scores (p. 203 Q 8) – mean 500 – st dev 100 What % score above 625? Translate 625 into z score (625-500) / 100 = 1.25 Use table: Z 1.25 – Area B.3944 (.5 +.3994 =.8944 = 89.44 th percentile – Area C.1056 (10.56% of scores higher)

49. Percentiles SAT scores – mean 500 – st dev 100 What percent between 400 and 600? – Find Z for 400 – Find Z for 600 – Use table