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Is there a covariate?

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Decision-Based Learning - Is there a covariate?

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Is there a covariate?

  1. 1. You will now determine if the problem you are working on has a covariate.
  2. 2. Here are your options:
  3. 3. Here are your options: There is a Covariate There is NO Covariate
  4. 4. What is a covariate?
  5. 5. The best way to explain a covariate is to show an example.
  6. 6. Imagine you want to know the effect of gender on hand writing neatness scores.
  7. 7. Imagine you want to know the effect of gender on hand writing neatness scores.
  8. 8. Imagine you want to know the effect of gender on hand writing neatness scores. And you find that females tend to get higher handwriting neatness scores than males.
  9. 9. But then you ask yourself. What if age were added to the mix? Does the age of the male or the female have an effect? Is there a way to see what the difference would be if we eliminated the age effect?
  10. 10. But then you ask yourself. What if age were added to the mix? Does the age of the male or the female have an effect? Is there a way to see what the difference would be if we eliminated the age effect?
  11. 11. But then you ask yourself. What if age were added to the mix? If you took out the effect for age, would the gender difference be the same?
  12. 12. But then you ask yourself. What if age were added to the mix? If you took out the effect for age, would the gender difference be the same? Is there a way to see what the difference would be for neatness scores between genders if we eliminated the age effect?
  13. 13. So, let’s say the average handwriting scores (on a scale from 1-10) for females and males are as follows:
  14. 14. Average female handwriting scores: 9.3
  15. 15. Average female handwriting scores: 9.3 Average male handwriting scores: 7.9
  16. 16. Average female handwriting scores: 9.3 Average male handwriting scores: 7.9 So, it looks like females have better handwriting scores.
  17. 17. But let’s say age also has a big effect on handwriting neatness.
  18. 18. Meaning that the older you are, the better your handwriting, regardless of whether you are female or male.
  19. 19. One statistical analysis that you will learn can adjust the average between female and male handwriting scores – after taking out the effect for age.
  20. 20. Here would be the adjusted average scores after controlling for age:
  21. 21. Before controlling for age:
  22. 22. Before controlling for age: Female handwriting average score: 9.3
  23. 23. Before controlling for age: Female handwriting average score: 9.3 Male handwriting average score: 7.9
  24. 24. Before controlling for age: Female handwriting average score: 9.3 Male handwriting average score: 7.9 After controlling for age:
  25. 25. Before controlling for age: Female handwriting average score: 9.3 Male handwriting average score: 7.9 After controlling for age: Female handwriting average score: 8.5
  26. 26. Before controlling for age: Female handwriting average score: 9.3 Male handwriting average score: 7.9 After controlling for age: Female handwriting average score: 8.5 Male handwriting average score: 8.4
  27. 27. Based on these results it appears that if you control for age, that gender does not have as big of an effect on handwriting neatness scores.
  28. 28. Consider this illustration of the idea of a covariate.
  29. 29. Let’s imagine that a group of people is struggling with boredom in a university class.
  30. 30. Let’s imagine that a group of people is struggling with boredom in a university class.
  31. 31. So, they decide to seek help from a therapist as well as take medication for it.
  32. 32. So, they decide to seek help from a therapist as well as take medication for it.
  33. 33. Afterwards, you have them take a survey testing their level of interest in a boring lecture.
  34. 34. Afterwards, you have them take a survey testing their level of interest in a boring lecture.
  35. 35. And you find that they have a pretty high interest score:
  36. 36. And you find that they have a pretty high interest score: Interest score = 30 (out of 40)
  37. 37. But your not sure if it was the therapy or the medication that had the biggest impact on the survey results.
  38. 38. But your not sure if it was the therapy or the medication that had the biggest impact on the survey results.
  39. 39. So, you make the therapy a covariate to see what the unique effect medication has on interest without the therapy.
  40. 40. And it turns out that if you eliminate the therapy, the results with just taking the medication alone are much less:
  41. 41. And it turns out that if you eliminate the therapy, the results with just taking the medication alone are much less: BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40)
  42. 42. And it turns out that if you eliminate the therapy, the results with just taking the medication alone are much less: BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40)
  43. 43. And it turns out that if you eliminate the therapy, the results with just taking the medication alone are much less: BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40) AFTER you eliminate the effect of the therapy Interest score = 20 (out of 40)
  44. 44. And it turns out that if you eliminate the therapy, the results with just taking the medication alone are much less: BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40) AFTER you eliminate the effect of the therapy Interest score = 20 (out of 40)
  45. 45. Therefore, therapy becomes the covariate whose effect we are eliminating to see the unique effect of just medication on interest. BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40) AFTER you eliminate the effect of the therapy Interest score = 20 (out of 40)
  46. 46. Therefore, therapy becomes the covariate that whose effect we are eliminating to see the unique effect of just medication on interest. BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40) AFTER you eliminate the effect of the therapy Interest score = 20 (out of 40)
  47. 47. Therefore, therapy becomes the covariate that whose effect we are eliminating to see the unique effect of just medication on interest. BEFORE you eliminate the effect of the therapy Interest score = 30 (out of 40) AFTER you eliminate the effect of the therapy Interest score = 20 (out of 40)
  48. 48. So, what does a word problem with a covariate look like?
  49. 49. Example 1:
  50. 50. A herd of horses are tested for their agility in an obstacle course.
  51. 51. A herd of horses are tested for their agility in an obstacle course. A certain breed tends to out perform another breed.
  52. 52. A herd of horses are tested for their agility in an obstacle course. A certain breed tends to out perform another breed. What are the results after eliminating the effect of where they were bred (either on the east or on the west coast)?
  53. 53. A herd of horses are tested for their agility in an obstacle course. A certain breed tends to out perform another breed. What are the results after eliminating the effect of where they were bred (either on the east or on the west coast)? “Eliminating the effect of” is an expression that signals the presence of a covariate
  54. 54. A herd of horses are tested for their agility in an obstacle course. A certain breed tends to out perform another breed. What are the results after eliminating the effect of where they were bred (either on the east or on the west coast)? What’s being controlled for is where the horses are bred.
  55. 55. A herd of horses are tested for their agility in an obstacle course. A certain breed tends to out perform another breed. What are the results after eliminating the effect of where they were bred (either on the east or on the west coast)? Does where horses were bred (the covariate) effect horse performance as much or more than their type of breed?
  56. 56. Example 2:
  57. 57. A pizza café owner wants to know who to market her pizza to.
  58. 58. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices:
  59. 59. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players.
  60. 60. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players. She decides to control for their year in school (upper or lower-classmen).
  61. 61. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players. She decides to control for their year in school (upper or lower-classmen). “Control for” is a phrase that generally means you have a covariate
  62. 62. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players. She decides to control for their year in school (upper or lower-classmen). It essentially has the same meaning as “Eliminating the effect of”
  63. 63. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players. She decides to control for their year in school (upper or lower-classmen). What’s being controlled for is year in school.
  64. 64. A pizza café owner wants to know who to market her pizza to. She devises a test to determine who eats more pizza slices: Football, Basketball, or Soccer players. She decides to control for their year in school (upper or lower-classmen). Does year in school effect the amount of pizza slices eaten as much or more than the type of athlete you are?
  65. 65. Example 3:
  66. 66. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy.
  67. 67. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey.
  68. 68. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey. After determining the difference between the groups, you have been asked to hold constant the video game playing by asking each teenager how much video gaming they engage in.
  69. 69. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey. After determining the difference between the groups, you have been asked to hold constant video game playing by asking each teenager how much video gaming they engage in. “Hold constant” is another way of saying “eliminating the effect of”.
  70. 70. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey. After determining the difference between the groups, you have been asked to hold constant video game playing by asking each teenager how much video gaming they engage in. This also is a signal that there is a covariate.
  71. 71. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey. After determining the difference between the groups, you have been asked to hold constant video game playing by asking each teenager how much video gaming they engage in. We are eliminating the effect of video game playing.
  72. 72. An anti-boredom therapy was used with a group of teenagers, while another group of teenagers did not receive any such therapy. To test their degree of boredom the groups listen to a statistics lecture for 1 hour and then are administered a boredom survey. After determining the difference between the groups, you have been asked to hold constant video game playing by asking each teenager how much video gaming they engage in. Does video gaming effect degree of boredom as much or more than the anti-boredom therapy?
  73. 73. Note - Not all covariate problems will use these expressions: • control for, • eliminate the effect of, or • partial out
  74. 74. Note - Not all covariate problems will use these expressions: • control for, • eliminate the effect of, or • partial out
  75. 75. Note - Not all covariate problems will use these expressions: • control for, • eliminate the effect of, or • partial out
  76. 76. Note - Not all covariate problems will use these expressions: • control for, • eliminate the effect of, or • partial out
  77. 77. Note - Not all covariate problems will use these expressions: • control for, • eliminate the effect of, or • partial out, • hold constant
  78. 78. But if the word problem has to do with looking at the degree to which there is an effect (e.g., boredom) when you take away the effect of something else (e.g., video-gaming), then you most likely have a covariate.
  79. 79. Which option is most appropriate for the problem you are working on:
  80. 80. Which option is most appropriate for the problem you are working on: There is a Covariate There is NO Covariate

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