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

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

9. Population and Sample Means

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

12. Assessing Dispersion by Looking at Spread 258258 Data Mean = 5

13. Assessing Dispersion by Looking at Spread 258258 Data Mean = 5 How far from the mean are the data?

14. Starting to Assess the Variance 258258 - 5 = - 3 = 0 = 3

15. = - 3 = 0 = 3 A Formula to Assess the Variance 258258 - 5 9 0 9

16. = - 3 = 0 = 3 A Formula to Assess the Variance 258258 - 5 9 0 9 = 18

17. = - 3 = 0 = 3 A Formula to Assess the Variance 258258 - 5 9 0 9 = 18

18. = - 3 = 0 = 3 A Formula to Assess the Variance 258258 - 5 9 0 9 = 18 THE VARIANCE

19. Sample and Population Standard Deviations

20. SAMPLE AND POPULATION TERMS SamplePopulation

21. SAMPLE AND POPULATION TERMS SamplePopulation Mean

22. SAMPLE AND POPULATION TERMS SamplePopulation Mean Variance

23. SAMPLE AND POPULATION TERMS SamplePopulation Mean Variance Standard Deviation

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

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

26. Standard Normal Curve

27. = 0 = 1 - 3  + 3 

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

29. or

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

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

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

34. Correlations

35. Correlation Example 1234512345 3475634756 Speaking Skill X Writing Skill Y

36. Correlation Chart Speaking Skill Writing skill 0 1 2 3 4 5 6 7 012345 * * * * *

37. Correlation Chart Speaking Skill Writing skill 0 1 2 3 4 5 6 7 012345 * * * * *

38. Correlation Chart Speaking Skill Writing skill 0 1 2 3 4 5 6 7 012345 * * * * *

39. Correlation Example Using z scores 1234512345 3475634756 Speaking Skill X Writing Skill Y - 1.27 -.63 0.63 1.27 - 1.27 -.63 1.27 0.63 Zx Zy

40. Correlation Example Using z scores 1234512345 3475634756 Speaking Skill X Writing Skill Y - 1.27 -.63 0.63 1.27 - 1.27 -.63 1.27 0.63 Zx Zy 1.61.4 0.8 Zx * Zy

41. Correlation Example Using z scores 1234512345 3475634756 Speaking Skill X Writing Skill Y - 1.27 -.63 0.63 1.27 - 1.27 -.63 1.27 0.63 Zx Zy 1.61.4 0.8 Zx * Zy SUM = _ 2.81 __ n-1 = 4

42. Correlation Example Using z scores 1234512345 3475634756 Speaking Skill X Writing Skill Y - 1.27 -.63 0.63 1.27 - 1.27 -.63 1.27 0.63 Zx Zy 1.61.4 0.8 Zx * Zy SUM = _ 2.81 __ n-1 = 4 =.70

43. Correlation Example 1234512345 3475634756 Speaking Skill X Writing Skill Y - 2 - 1 0 1 2 - 2 - 1 2 0 1

44. Correlation Example 1234512345 3475634756 Speaking Skill X Writing Skill Y - 2 - 1 0 1 2 - 2 - 1 2 0 1 * 4 1 0 2

45. Correlation Example 1234512345 3475634756 Speaking Skill X Writing Skill Y - 2 - 1 0 1 2 - 2 - 1 2 0 1 * 4 1 0 2 = 7

46. Correlation Example 1234512345 3475634756 Speaking Skill X Writing Skill Y - 2 - 1 0 1 2 - 2 - 1 2 0 1 * 4 1 0 2 = 7 n-1 = 4

47. Correlation Computation