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Practice

theodorearthur
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Practice

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  1. With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. Determine if customers should be happy about paying more.

  2. Practice • Situation 1 • Based on a sample of 100 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero. • Situation 2 • Based on a sample of 600 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero.

  3. Step 1 • Situation 1 • H1: r is not equal to 0 • The two variables are related to each other • H0: r is equal to zero • The two variables are not related to each other • Situation 2 • H1: r is not equal to 0 • The two variables are related to each other • H0: r is equal to zero • The two variables are not related to each other

  4. Step 2 • Situation 1 • df = 98 • t crit = +1.985 and -1.984 • Situation 2 • df = 598 • t crit = +1.96 and -1.96

  5. Step 3 • Situation 1 • r = .15 • Situation 2 • r = .15

  6. Step 4 • Situation 1 • Situation 2

  7. Step 5 • Situation 1 • 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 • Situation 2 • 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

  8. Step 6 • Situation 1 • Based on a sample of 100 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero. • There is not a significant relationship between extraversion and happiness • Situation 2 • Based on a sample of 600 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero. • There is a significant relationship between extraversion and happiness.

  9. Practice • You collect data from 53 females and find the correlation between candy and depression is -.40. Determine if this value is significantly different than zero. • You collect data from 53 males and find the correlation between candy and depression is -.50. Determine if this value is significantly different than zero.

  10. Practice • You collect data from 53 females and find the correlation between candy and depression is -.40. • t obs = 3.12 • t crit = 2.00 • You collect data from 53 males and find the correlation between candy and depression is -.50. • t obs = 4.12 • t crit = 2.00

  11. Practice • You collect data from 53 females and find the correlation between candy and depression is -.40. • You collect data from 53 males and find the correlation between candy and depression is -.50. • Is the effect of candy significantly different for males and females?

  12. Hypothesis • H1: the two correlations are different • H0: the two correlations are not different

  13. Testing Differences Between Correlations • Must be independent for this to work

  14. When the population value of r is not zero the distribution of r values gets skewed Easy to fix! Use Fisher’s r transformation Page 746

  15. Testing Differences Between Correlations • Must be independent for this to work

  16. Testing Differences Between Correlations

  17. Testing Differences Between Correlations

  18. Testing Differences Between Correlations

  19. Testing Differences Between Correlations Note: what would the z value be if there was no difference between these two values (i.e., Ho was true)

  20. Testing Differences • Z = -.625 • What is the probability of obtaining a Z score of this size or greater, if the difference between these two r values was zero? • p = .267 • If p is < .025 reject Ho and accept H1 • If p is = or > .025 fail to reject Ho • The two correlations are not significantly different than each other!

  21. Remember this: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)

  22. Regression allows us to predict! . . . . .

  23. Straight Line Y = mX + b Where: Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

  24. Excel Example

  25. That’s nice but. . . . • How do you figure out the best values to use for m and b ? • First lets move into the language of regression

  26. Straight Line Y = mX + b Where: Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

  27. Regression Equation Y = a + bX Where: Y = value predicted from a particular X value a = point at which the regression line intersects the Y axis b = slope of the regression line X = X value for which you wish to predict a Y value

  28. Practice • Y = -7 + 2X • What is the slope and the Y-intercept? • Determine the value of Y for each X: • X = 1, X = 3, X = 5, X = 10

  29. Practice • Y = -7 + 2X • What is the slope and the Y-intercept? • Determine the value of Y for each X: • X = 1, X = 3, X = 5, X = 10 • Y = -5, Y = -1, Y = 3, Y = 13

  30. Finding a and b • Uses the least squares method • Minimizes Error Error = Y - Y  (Y - Y)2 is minimized

  31. . . . . .

  32. Error = Y - Y  (Y - Y)2 is minimized . Error = 1 . Error = .5 . . Error = -1 . Error = 0 Error = -.5

  33. Finding a and b • Ingredients • COVxy • Sx2 • Mean of Y and X

  34. Regression

  35. Regression Ingredients Mean Y =4.6 Mean X = 3 Covxy = 3.75 S2X = 2.50

  36. Regression Ingredients Mean Y =4.6 Mean X = 3 Covxy = 3.75 S2x = 2.50

  37. Regression Ingredients Mean Y =4.6 Mean X = 3 Covxy = 3.75 S2x = 2.50

  38. Regression Equation Y = a + bx Equation for predicting smiling from talking Y = .10+ 1.50(x)

  39. Regression Equation Y = .10+ 1.50(x) How many times would a person likely smile if they talked 15 times?

  40. Regression Equation Y = .10+ 1.50(x) How many times would a person likely smile if they talked 15 times? 22.6 = .10+ 1.50(15)

  41. Y = 0.1 + (1.5)X . . . . .

  42. Y = 0.1 + (1.5)XX = 1; Y = 1.6 . . . . . .

  43. Y = 0.1 + (1.5)XX = 5; Y = 7.60 . . . . . . .

  44. Y = 0.1 + (1.5)X . . . . . . .

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