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

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

6. Bivariate Distribution

7. Positive Correlation

8. Positive Correlation

9. Regression Line

10. Correlation
r = 1.00

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

12. Regression Line . . . . .
r = .64

14. Negative Correlation

15. Negative Correlation
r =

16. Negative Correlation . . .
r = - .85 . .

18. Zero Correlation

19. Zero Correlation . . . . .
r = .00

20. 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)

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

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

23. 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

24. Practice
#6.8
#6.5 1) Draw a scatter plot
2) Estimate the correlation

25. 6.8
A) -.60
B) -.95
C) .50
D) .25

26. 6.5
r = .51

28. . . . . .

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. Correlation Coefficient
A correlation coefficient provides a quantitative way to express the degree of relationship between two variables
There are 3 different formulas presented in the book
Z-score formula is a good way to see “what's going on”

31. Blanched Formula
r =
XY = product of each X value multiplied by its paired Y value
X = mean of variable X
Y = mean of variable Y
Sx = standard deviation of variable X
Sy = standard deviation of variable Y
N = number of pairs of observations

33. Mean Y = 4.6; SY = 2.41 Mean X = 3.0; SX = 1.41

34. Mean Y = 4.6; SY = 2.41 Mean X = 3.0; SX = 1.41

35. r = Blanched Formula XY = 84 X = 3.0 Y = 4.6 Sx = 1.41 Sy = 2.41

36. r = Blanched Formula 84 XY = 84 X = 3.0 Y = 4.6 Sx = 1.41 Sy = 2.41

37. r = Blanched Formula 84 3.0 4.6 XY = 84 X = 3.0 Y = 4.6 Sx = 1.41
Sy = 2.41
N = 5

38. r = Blanched Formula 84 3.0 4.6 5 1.41 2.41 XY = 84 X = 3.0 Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5

39. r = Blanched Formula 84 3.0 4.6 16.8 13.8 5 1.41 2.41 XY = 84 X = 3.0
Sx = 1.41
Sy = 2.41
N = 5

40. Blanched Formula 84
3.0
4.6
16.8
13.8
3.00 5
r =
.88
2.41
3.40
1.41
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5

42. Practice
What is the relationship between aggression and happiness?

43. Mean aggression = 14. 50; Saggression = 4. 43 Mean happiness = 6
Mean aggression = 14.50; Saggression = 4.43 Mean happiness = 6.00; Shappiness = 2.16

44. Mean aggression = 14. 50; Saggression = 4. 43 Mean happiness = 6
Mean aggression = 14.50; Saggression = 4.43 Mean happiness = 6.00; Shappiness = 2.16

45. r = Blanched Formula XY = 326 X = 6.0 Y = 14.50 Sx = 2.16 Sy = 4.43

46. -.57 = Blanched Formula 326 6.0 14.5 4 2.16 4.43 XY = 326 X = 6.0
Sx = 2.16
Sy = 4.43
N = 4