Decision-Based Learning - Is there a covariate?

1. You will now determine if the problem you are working on
has a covariate.

2. Here are your options:

3. Here are your options:
There is a Covariate
There is NO Covariate

4. What is a covariate?

5. The best way to explain a covariate is to show an example.

6. Imagine you want to know the effect of gender
on hand writing neatness scores.

7. Imagine you want to know the effect of gender
on hand writing neatness scores.

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. 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. 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. 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. 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. So, let’s say the average handwriting scores (on
a scale from 1-10) for females and males are as
follows:

14. Average female handwriting scores: 9.3

15. Average female handwriting scores: 9.3
Average male handwriting scores: 7.9

16. Average female handwriting scores: 9.3
Average male handwriting scores: 7.9
So, it looks like females have better handwriting
scores.

17. But let’s say age also has a big effect on
handwriting neatness.

18. Meaning that the older you are, the better your
handwriting, regardless of whether you are
female or male.

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. Here would be the adjusted average scores after
controlling for age:

21. Before controlling for age:

22. Before controlling for age:
Female handwriting average score: 9.3

23. Before controlling for age:
Female handwriting average score: 9.3
Male handwriting average score: 7.9

24. Before controlling for age:
Female handwriting average score: 9.3
Male handwriting average score: 7.9
After controlling for age:

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. 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. 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. Consider this illustration of the idea of a
covariate.

29. Let’s imagine that a group of people is struggling
with boredom in a university class.

30. Let’s imagine that a group of people is struggling
with boredom in a university class.

31. So, they decide to seek help from a therapist as
well as take medication for it.

32. So, they decide to seek help from a therapist as
well as take medication for it.

33. Afterwards, you have them take a survey testing
their level of interest in a boring lecture.

34. Afterwards, you have them take a survey testing
their level of interest in a boring lecture.

35. And you find that they have a pretty high
interest score:

36. And you find that they have a pretty high
interest score:
Interest score = 30 (out of 40)

37. But your not sure if it was the therapy or the
medication that had the biggest impact on the
survey results.

38. But your not sure if it was the therapy or the
medication that had the biggest impact on the
survey results.

39. So, you make the therapy a covariate to see
what the unique effect medication has on
interest without the therapy.

40. And it turns out that if you eliminate the
therapy, the results with just taking the
medication alone are much less:

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. 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. 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. 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. 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. 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. 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. So, what does a word problem with a covariate
look like?

49. Example 1:

50. A herd of horses are tested for their agility in an
obstacle course.

51. A herd of horses are tested for their agility in an
obstacle course. A certain breed tends to out
perform another breed.

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. 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. 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. 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. Example 2:

57. A pizza café owner wants to know who to
market her pizza to.

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. 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. 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. 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. 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. 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. 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. Example 3:

66. An anti-boredom therapy was used with a group
of teenagers, while another group of teenagers
did not receive any such therapy.

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. 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. 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. 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. 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. 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. Note - Not all covariate problems will use these
expressions:
• control for,
• eliminate the effect of, or
• partial out

74. Note - Not all covariate problems will use these
expressions:
• control for,
• eliminate the effect of, or
• partial out

75. Note - Not all covariate problems will use these
expressions:
• control for,
• eliminate the effect of, or
• partial out

76. Note - Not all covariate problems will use these
expressions:
• control for,
• eliminate the effect of, or
• partial out

77. Note - Not all covariate problems will use these
expressions:
• control for,
• eliminate the effect of, or
• partial out,
• hold constant

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. Which option is most appropriate for the problem you are
working on:

80. Which option is most appropriate for the problem you are
working on:
There is a Covariate
There is NO Covariate