The document discusses covariates and how to determine if they are present in a problem. It uses an example of examining the relationship between socioeconomic status (SES) and student ACT scores, and whether parental status is a covariate. Adding parental status as a variable decreases the correlation between SES and ACT scores, showing it plays a role in explaining their relationship. Controlling for covariates allows viewing the unique relationship between variables when the covariate's effect is removed. Key terms that indicate a covariate is present include "control for", "hold constant", and "adjust for".

1. Are there covariates?

2. The purpose of this presentation is to help you
determine if there are covariates in the problem
you are working with.

3. The purpose of this presentation is to help you
determine if there are covariates in the problem
you are working with.
There ARE Covariates
or
There ARE NO Covariates

4. Here is an explanation of a covariate:

5. Let’s say you want to know the relationship
between X and Y.

6. Let’s say you want to know the relationship
between X and Y.
Is X related to Y ?

7. Let’s say you want to know the relationship
between X and Y.
Is X related to Y ?
Z But, you wonder if might explain
this relationship in part.

8. So you control for Z

9. . . . in order to see what the relationship would be
between and
if you took out the effect of

10. . . . in order to see what the relationship would be
X Y
between and
if you took out the effect of

11. . . . in order to see what the relationship would be
X Y
between and
if you took out the effect of
Z

12. Let’s consider this example:

13. Let’s say you want to know if there is a
relationship between socio-economic status and
student ACT scores.

14. Let’s say you want to know if there is a
relationship between socio-economic status and
student ACT scores.
Socio-economic
Is related to ACT ?
status
Scores

15. Let’s say you want to know if there is a
relationship between socio-economic status and
student ACT scores.
Socio-economic
Is related to ACT ?
status
Scores
But, you wonder if P arent status
might explain this relationship in part.

16. By parent status, we are referring to whether
there are two parents or a single parent in the
home.

17. Here is what the data set might look like:

18. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
A 3 26
B 2 22
C 3 25
D 1 21
E 1 19
F 2 21
G 1 25

19. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
A 3 26
B 2 22
C 3 25
D 1 21
E 1 19
F 2 21
G 1 25
Let’s say that the relationship
between these two variables is .85
(which we will explain in another
presentation - shows a strong
relationship)

20. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
A 3 26
B 2 22
C 3 25
D 1 21
E 1 19
F 2 21
G 1 25
But, what if
parent status
plays an
important role
in this
relationship?

21. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
Parent Status
1 = single
2 = two
A 3 26 2
B 2 22 2
C 3 25 2
D 1 21 1
E 1 19 1
F 2 21 1
G 1 25 2

22. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
Parent Status
1 = single
2 = two
A 3 26 2
B 2 22 2
C 3 25 2
D 1 21 1
E 1 19 1
F 2 21 1
G 1 25 2
After
controlling for
Parent Status
we find that
the correlation
drops from .85
to .62

23. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
Parent Status
1 = single
2 = two
A 3 26 2
B 2 22 2
C 3 25 2
D 1 21 1
E 1 19 1
F 2 21 1
G 1 25 2
This means that parent status plays an important
role in explaining the relationship between Socio-economic
Status and ACT Scores

24. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
Parent Status
1 = single
2 = two
A 3 26 2
B 2 22 2
C 3 25 2
D 1 21 1
E 1 19 1
F 2 21 1
G 1 25 2
By controlling for Parent Status we are able to see the
unique relationship between S.E.S and ACT Scores
when Parent Status is no longer a factor.

25. Here is what the data set might look like:
Student Socio-economic Status
1 = poor
2 = middle class
3 = wealthy
ACT
Scores
Parent Status
1 = single
2 = two
A 3 26 2
B 2 22 2
C 3 25 2
D 1 21 1
E 1 19 1
F 2 21 1
G 1 25 2
Parent Status is an example of what we call a
“COVARIATE”.

26. Here are some of the expressions you will find in
your word problem if a covariate is present:

27. Here are some of the expressions you will find in
your word problem if a covariate is present:
CONTROL FOR

28. Here are some of the expressions you will find in
your word problem if a covariate is present:
CONTROL FOR
HOLD CONSTANT

29. Here are some of the expressions you will find in
your word problem if a covariate is present:
CONTROL FOR
HOLD CONSTANT
ELIMINATE THE
EFFECT OF

30. Here are some of the expressions you will find in
your word problem if a covariate is present:
CONTROL FOR
HOLD CONSTANT
ELIMINATE THE
EFFECT OF
PARTIAL OUT

31. Here are some of the expressions you will find in
your word problem if a covariate is present:
CONTROL FOR
HOLD CONSTANT
ELIMINATE THE
EFFECT OF
PARTIAL OUT
ADJUST FOR

32. Now examine your word problem and
determine if . . .

33. Now examine your word problem and
determine if . . .
There ARE Covariates
or
There ARE NO Covariates