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

You can calculate: Central tendency Variability You could graph the data. You can calculate: Central tendency Variability You could graph the data. Bivariate Distribution. Positive Correlation. Positive Correlation. Regression Line. Correlation. r = 1.00. Regression Line. r = .64.

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

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

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

  3. Bivariate Distribution

  4. Positive Correlation

  5. Positive Correlation

  6. Regression Line

  7. Correlation r = 1.00

  8. Regression Line . . . . . r = .64

  9. Regression Line . . . . . r = .64

  10. Negative Correlation

  11. Negative Correlation r = - 1.00

  12. Negative Correlation . . . r = - .85 . .

  13. Zero Correlation

  14. Zero Correlation . . . . . r = .00

  15. 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)

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

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

  18. 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

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

  20. 6.8 • A) -.60 • B) -.95 • C) .50 • D) .25

  21. 6.5 • r = .51

  22. . . . . .

  23. 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)

  24. 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”

  25. 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

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

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

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

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

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

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

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

  33. 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

  34. Practice • What is the relationship between aggression and happiness?

  35. Mean aggression = 14.50; Saggression = 4.43Mean happiness = 6.00; Shappiness = 2.16

  36. Mean aggression = 14.50; Saggression = 4.43Mean happiness = 6.00; Shappiness = 2.16

  37. Blanched Formula r = XY = 326 X = 6.0 Y = 14.50 Sx = 2.16 Sy = 4.43 N = 4

  38. Blanched Formula 326 6.0 14.5 4 -.57 = 2.16 4.43 XY = 326 X = 6.0 Y = 14.50 Sx = 2.16 Sy = 4.43 N = 4

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