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 =

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 = 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 Candy Depression Charlie 5 55 Augustus 7 43 Veruca 4 59 Mike
108
Violet 65
Scandy = 1.52 Sdepression = 24.82

50. Practice Candy (X) Depression (Y) XY Charlie 5 55 275 Augustus 7 43
301
Veruca 4 59
236
Mike 3
108
324
Violet 65
260 ∑

51. Practice Candy (X) Depression (Y) XY Charlie 5 55 275 Augustus 7 43
301
Veruca 4 59
236
Mike 3
108
324
Violet 65
260 ∑ 23
330
1396

52. ∑XY = 1396
∑Y = 330
∑X = 23
N = 5

53. ∑XY = 1396
∑Y = 330
∑X = 23
N = 5

54. Correlation
COV = -30.5
Sx = 1.52
Sy = 24.82

55. Correlation
COV = -30.5
Sx = 1.52
Sy = 24.82

56. Hypothesis testing of r
Is there a significant relationship between X and Y (or are they independent)
Like the X2

57. Steps for testing r value
1) State the hypothesis
2) Find t-critical
3) Calculate r value
4) Calculate t-observed
5) Decision
6) Put answer into words

58. Practice
Determine if candy consumption is significantly related to depression.
Test at alpha = .05

59. Practice Candy Depression Charlie 5 55 Augustus 7 43 Veruca 4 59 Mike
108
Violet 65
Scandy = 1.52 Sdepression = 24.82

60. Step 1 H1: r is not equal to 0 H0: r is equal to zero
The two variables are related to each other
H0: r is equal to zero
The two variables are not related to each other

61. Step 2 Calculate df = N - 2 Page 747 First Column are df
Look at an alpha of .05 with two-tails

62. t distribution
df = 3

63. t distribution
tcrit =
tcrit = 3.182

64. t distribution
tcrit =
tcrit = 3.182

65. Step 3
COV = -30.5
Sx = 1.52
Sy = 24.82

66. Step 4
Calculate t-observed

67. Step 4
Calculate t-observed

68. Step 4
Calculate t-observed

69. Step 5 If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

70. t distribution
tcrit =
tcrit = 3.182

71. t distribution
tcrit =
tcrit = 3.182
-2.39

72. Step 5 If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

73. Step 6
Determine if candy consumption is significantly related to depression.
Test at alpha = .05
Candy consumption is not significantly related to depression
Note: this finding is due to the small sample size

74. SPSS

75. Practice
Is there a significant (.05) relationship between aggression and happiness?

76. Mean aggression = 14. 50; S2aggression = 19. 63 Mean happiness = 6
Mean aggression = 14.50; S2aggression = Mean happiness = 6.00; S2happiness = 4.67

77. Answer Cov = -7.33 r = -.76 t crit = 4.303 Thus, fail to reject Ho
Aggression was not significantly related to happiness

78. SPSS