You can calculate: Central tendency Variability You could graph the data

3. You can calculate: Central tendency Variability You could graph the data

4. You can calculate: Central tendency Variability You could graph the data

5. Bivariate Distribution

6. Positive Correlation

7. Positive Correlation

8. Regression Line

9. Correlation r = 1.00

10. Regression Line . . . . . r = .64

11. Regression Line . . . . . r = .64

12. Practice

13. Regression Line

14. Regression Line . . . . .

15. Regression Line . . . . .

17. Negative Correlation

18. Negative Correlation r = - 1.00

19. Negative Correlation . . . r = - .85 . .

21. Zero Correlation

22. Zero Correlation . . . . . r = .00

23. Correlation Coefficient • The sign of a correlation (+ or -) only tells you the direction of the relationship • The value of the correlation only tells you about the size of the relationship (i.e., how close the scores are to the regression line)

24. Excel Example

25. Which is a bigger effect? r = .40 or r = -.40 How are they different?

26. Interpreting an r value • What is a “big r” • Rule of thumb: Small r = .10 Medium r = .30 Large r = .50

27. Practice • Do you think the following variables are positively, negatively or uncorrelated to each other? • Alcohol consumption & Driving skills • Miles of running a day & speed in a foot race • Height & GPA • Forearm length & foot length • Test #1 score and Test#2 score

29. Statistics Needed • Need to find the best place to draw the regression line on a scatter plot • Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)

30. Covariance • Correlations are based on the statistic called covariance • Reflects the degree to which two variables vary together • Expressed in deviations measured in the original units in which X and Y are measured

31. Note how it is similar to a variance • If Ys were changed to Xs it would be s2 • How it works (positive vs. negative vs. zero)

32. Computational formula

33. Ingredients: ∑XY ∑X ∑Y N

36. N = 5

37. ∑XY = 84 ∑Y = 23 ∑X = 15 N = 5

38. ∑XY = 84 ∑Y = 23 ∑X = 15 N = 5

39. ∑XY = 84 ∑Y = 23 ∑X = 15 N = 5

40. ∑XY = 84 ∑Y = 23 ∑X = 15 N = 5

41. ∑XY = 84 ∑Y = 23 ∑X = 15 N = 5

42. Problem! • The size of the covariance depends on the standard deviation of the variables • COVXY = 3.75 might occur because • There is a strong correlation between X and Y, but small standard deviations • There is a weak correlation between X and Y, but large standard deviations

43. Solution • Need to “standardize” the covariance • Remember how we standardized single scores

44. Correlation

46. Correlation

47. Correlation

48. Practice • You are interested in if candy intake is related to childhood depression. You collect data from 5 children.

49. Practice Scandy = 1.52 Sdepression = 24.82

50. Practice