Introduction to Using Statistical Analyses

2. Introduction to Using Statistical Analyses • Measures of Central Tendency (done . . .for now) • Measures of Variability • Writing • Using the Standard Normal Curve

3. A Reminder of the Way We Note Things: Our Shorthand

4. A Reminder of the Way We Note Things: Our Shorthand

5. A Reminder of the Way We Note Things: Our Shorthand

6. A Reminder of the Way We Note Things: Our Shorthand

7. A Reminder of the Way We Note Things: Our Shorthand

8. Population and Sample Means

9. Population and Sample Means

10. Introduction to Using Statistical Analyses • Measures of Central Tendency (done . . .for now) • Measures of Variability • Writing • Using the Standard Normal Curve

11. Assessing Dispersion by Looking at Spread Data 2 5 8 Mean = 5

12. Assessing Dispersion by Looking at Spread Data 2 5 8 Mean = 5 How far from the mean are the data?

13. Starting to Assess the Variance 2 5 8 - 5 - 5 - 5 = - 3 = 0 = 3

14. A Formula to Assess the Variance 2 5 8 - 5 - 5 - 5 = - 3 = 0 = 3 9 0 9

15. A Formula to Assess the Variance 2 5 8 - 5 - 5 - 5 = - 3 = 0 = 3 9 0 9 18 =

16. A Formula to Assess the Variance 2 5 8 - 5 - 5 - 5 = - 3 = 0 = 3 9 0 9 18 =

17. A Formula to Assess the Variance 2 5 8 - 5 - 5 - 5 = - 3 = 0 = 3 9 0 9 THE VARIANCE 18 =

18. Sample and Population Standard Deviations

19. SAMPLE AND POPULATION TERMS Sample Population

20. SAMPLE AND POPULATION TERMS Sample Population Mean

21. SAMPLE AND POPULATION TERMS Sample Population Mean Variance

22. SAMPLE AND POPULATION TERMS Sample Population Mean Variance Standard Deviation

23. Introduction to Using Statistical Analyses • Measures of Central Tendency (done . . .for now) • Measures of Variability • Writing • Using the Standard Normal Curve

24. Introduction to Using Statistical Analyses • Measures of Central Tendency (done . . .for now) • Measures of Variability • Writing • Using the Standard Normal Curve

25. Standard Normal Curve

26. Standard Normal Curve = 0 - 3 s + 3 s = 1

27. z Scores when Data Do Not Already Have a Mean of 0 and a Standard Deviation of 1

28. z Scores when Data Do Not Already Have a Mean of 0 and a Standard Deviation of 1 or

29. Areas under the Standard Normal Curve z = -1.67 z = 1 0

30. Areas under the Standard Normal Curve z = -1.75 z = 1.75 0

31. Areas under the Standard Normal Curve z = 1 0

33. Correlations

34. Correlation Example Speaking Skill X Writing Skill Y 1 2 3 4 5 3 4 7 5 6

35. Correlation Chart * 7 * 6 * 5 * 4 Writing skill * 3 2 1 0 0 1 2 3 4 5 Speaking Skill

36. Correlation Chart * 7 * 6 * 5 * 4 Writing skill * 3 2 1 0 0 1 2 3 4 5 Speaking Skill

37. Correlation Chart * 7 * 6 * 5 * 4 Writing skill * 3 2 1 0 0 1 2 3 4 5 Speaking Skill

38. Correlation Example Using z scores Speaking Skill X Writing Skill Y Zy Zx 1 2 3 4 5 - 1.27 - .63 0 .63 1.27 3 4 7 5 6 - 1.27 - .63 1.27 0 .63

39. Correlation Example Using z scores Speaking Skill X Writing Skill Y Zy Zx Zx * Zy 1 2 3 4 5 - 1.27 - .63 0 .63 1.27 3 4 7 5 6 - 1.27 - .63 1.27 0 .63 1.61 .4 0 0 .8

40. Correlation Example Using z scores Speaking Skill X Writing Skill Y Zy Zx Zx * Zy 1 2 3 4 5 - 1.27 - .63 0 .63 1.27 3 4 7 5 6 - 1.27 - .63 1.27 0 .63 1.61 .4 0 0 .8 SUM = _ 2.81 __ n-1 = 4

41. Correlation Example Using z scores Speaking Skill X Writing Skill Y Zy Zx Zx * Zy 1 2 3 4 5 - 1.27 - .63 0 .63 1.27 3 4 7 5 6 - 1.27 - .63 1.27 0 .63 1.61 .4 0 0 .8 =.70 SUM = _ 2.81 __ n-1 = 4

42. Correlation Example Speaking Skill X Writing Skill Y 1 2 3 4 5 - 2 - 1 0 1 2 3 4 7 5 6 - 2 - 1 2 0 1

43. Correlation Example Speaking Skill X Writing Skill Y * 1 2 3 4 5 - 2 - 1 0 1 2 3 4 7 5 6 - 2 - 1 2 0 1 4 1 0 0 2

44. Correlation Example Speaking Skill X Writing Skill Y * 1 2 3 4 5 - 2 - 1 0 1 2 3 4 7 5 6 - 2 - 1 2 0 1 4 1 0 0 2 = 7

45. Correlation Example Speaking Skill X Writing Skill Y * 1 2 3 4 5 - 2 - 1 0 1 2 3 4 7 5 6 - 2 - 1 2 0 1 4 1 0 0 2 = 7 n-1 = 4

46. Correlation Computation

47. Correlation Computation

48. Correlation Computation

49. Correlation Computation

50. Correlation Computation