The document discusses dependent variables in statistics problems. It explains that the dependent variable is the "effect" side of a cause-and-effect relationship, or the "influenced" side of an influencer-influenced relationship. Several examples are provided to demonstrate how to identify the dependent variable in word problems involving research studies. The dependent variable is the main outcome or variable being measured in response to changes in other variables. Problems can have either a single dependent variable or multiple dependent variables.

1. The purpose of this presentation is to assist you
in determining the number of dependent
variables in the problem you are working on.

2. Here are your options:

3. Here are your options:
1 Dependent Variable
2+ Dependent Variables

4. In statistics we are generally attempting to
determine what causes what?

5. In statistics we are generally attempting to
determine what causes what?
Cause

6. In statistics we are generally attempting to
determine what causes what?
Cause

7. In statistics we are generally attempting to
determine what causes what?
Cause Effect

8. Or what influences what?

9. Or what influences what?
Influencer Influenced

10. Or what influences what?
Influencer Influenced

11. Or what influences what?
Influencer Influenced

12. Simply put, in the cause and effect model, the
effect side of the equation is known as the
dependent variable.

13. Simply put, in the cause and effect model, the
effect side of the equation is known as the
dependent variable.
Effect
Cause

14. Simply put, in the cause and effect model, the
effect side of the equation is known as the
dependent variable.
Effect
Cause

15. Simply put, in the cause and effect model, the
effect side of the equation is known as the
dependent variable.
Effect
Cause
Dependent
Variable

16. Or in the influencer / influenced model, the
influenced side of the equation is also known as
the dependent variable.

17. Or in the influencer / influenced model, the
influenced side of the equation is also known as
the dependent variable.
Influencer Influenced

18. Or in the influencer / influenced model, the
influenced side of the equation is also known as
the dependent variable.
Influencer Influenced

19. Or in the influencer / influenced model, the
influenced side of the equation is also known as
the dependent variable.
Influencer Influenced
Dependent
Variable

20. Let’s look at an example:

21. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.

22. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
What is being influenced here?

23. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
What is being influenced here?

24. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
This is the Dependent Variable

25. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
What is the influencer?

26. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
What is the influencer?

27. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.

28. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
Influencer Influenced

29. A researcher wishes to determine the degree to which
test scores are influenced by amount of study time.
Dependent
Variable
Influencer

30. Let’s look at another example almost identical to
the last one.

31. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.

32. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
What is being influenced here?

33. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
What is being influenced here?

34. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
This is the Dependent Variable

35. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
What is the influencer?

36. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
What is the influencer?

37. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.

38. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Influencer Influenced

39. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Influencer Influenced

40. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Influencer Test Scores

41. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Influencer Test Scores
The Dependent Variable

42. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Influencer Test Scores

43. A researcher wishes to determine the degree to which
test scores are influenced by amount of sleep.
Test Scores
Amount of
Sleep

44. Let’s see how this question could be worded as
an actual study.

45. Researchers wish to determine if the amount of
sleep can have an effect on test scores.

46. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups.

47. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.

48. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.

49. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.
What is being influenced here?

50. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.
What is being influenced here?

51. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.
This is the DEPENDENT VARIABLE

52. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.
What is doing the influencing?

53. Researchers wish to determine if the amount of
sleep can have an effect on test scores. So, they
randomly select two similar groups. They
ensure that one group gets 6-8 hours of sleep
and a second group gets only 3-4 hours of sleep.
That morning both groups are administered an
academic test. The results are examined for
differences.
What is doing the influencing?

54. See if you can identify the dependent variable in
the following research studies.

55. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.

56. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.

57. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.
This is the DEPENDENT VARIABLE

58. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.

59. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.
This is the DEPENDENT VARIABLE

60. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health.
- an instructional software helps students
overcome conceptual gaps.

61. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.
This is the DEPENDENT VARIABLE

62. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health.
- an instructional software helps students
overcome conceptual gaps.

63. Scientist wish to determine if -
- good nutrition results in increased longevity.
- time on social media impacts verbal skills.
- exercise effects heart health
- an instructional software helps students
overcome conceptual gaps.
This is the DEPENDENT VARIABLE

64. Now, see if you can identify the dependent
variables in the following word problems:

65. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period.

66. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:

67. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:
Amount of Stress
Negligible
stress
Minimal
stress
Moderate
stress
Sever
stress
Number of
viral
infections
2 4 6 5
1 3 5 7
4 2 7 8
1 3 5 4

68. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:
What is being influenced here?
Amount of Stress
Negligible
stress
Minimal
stress
Moderate
stress
Sever
stress
Number of
viral
infections
2 4 6 5
1 3 5 7
4 2 7 8
1 3 5 4

69. A researcher investigated the number of viral
infections people contract as a function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:
What is being influenced here?
Amount of Stress
Negligible
stress
Minimal
stress
Moderate
stress
Sever
stress
Number of
viral
infections
2 4 6 5
1 3 5 7
4 2 7 8
1 3 5 4

70. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:
What is being influenced here?
Amount of Stress
Negligible
stress
Minimal
stress
Moderate
stress
Sever
stress
Number of
viral
infections
2 4 6 5
1 3 5 7
4 2 7 8
1 3 5 4

71. A researcher investigated the number of viral
infections people contract as function of the
amount of stress they experienced during a six-month
period. She obtained the following data
set:
This is the DEPENDENT VARIABLE
Amount of Stress
Negligible
stress
Minimal
stress
Moderate
stress
Sever
stress
Number of
viral
infections
2 4 6 5
1 3 5 7
4 2 7 8
1 3 5 4

72. Next example:

73. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task.

74. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:

75. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:
Levels of Volume
Low
Volume
Moderate
Volume
High
Volume
Number of
errors
2 4 6
1 3 5
4 2 7
1 3 5

76. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:
What is being influenced here?
Levels of Volume
Low
Volume
Moderate
Volume
High
Volume
Number of
errors
2 4 6
1 3 5
4 2 7
1 3 5

77. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:
What is being influenced here?
Levels of Volume
Low
Volume
Moderate
Volume
High
Volume
Number of
errors
2 4 6
1 3 5
4 2 7
1 3 5

78. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:
What is being influenced here?
Levels of Volume
Low
Volume
Moderate
Volume
High
Volume
Number of
errors
2 4 6
1 3 5
4 2 7
1 3 5

79. A researcher investigated the effect of volume
background noise on participant’s error rates
while performing a boring task. She tested
three groups of randomly selected students and
obtained the following error data:
This is the DEPENDENT VARIABLE
Levels of Volume
Low
Volume
Moderate
Volume
High
Volume
Number of
errors
2 4 6
1 3 5
4 2 7
1 3 5

80. Next example:

81. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.

82. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
What is being influenced here?

83. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
What is being influenced here?

84. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
This is the DEPENDENT VARIABLE

85. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
In this case there are two influencers

86. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
In this case there are two influencers

87. A researcher investigated the effects of
(1) whether participants meditate, and (2) the
degree of introversion they exhibit on hypnotic
suggestibility.
In this case there are two influencers

88. All of the examples shown so far are examples of
problems with only one dependent variable.

89. What does a word problem look like with more
than one dependent variable?

90. Here are some examples:

91. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.

92. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.
What is being influenced here?

93. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.
1st
Dependent
Variable
What is being influenced here?

94. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.
2nd
Dependent
Variable
What is being influenced here?

95. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.
What is doing the influencing?

96. You have been asked to determine the degree to
which the amount of sleep effects students both
academically and socially.
What is doing the influencing?

97. This next example has more complicated
wording, but you should be able to identify the
dependent variable:

98. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.

99. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.
What is being influenced here?

100. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.
1st
Dependent
Variable
What is being influenced here?

101. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.
2nd
Dependent
Variable
What is being influenced here?

102. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.
What is doing the influencing?

103. You have been asked to determine how the
process known as fracking impacts the
subterranean as well as the above ground
environments.
What is doing the influencing?

104. Quick note -

105. Quick note – there will be some research questions
that only have a dependent variable (the thing
being influenced) without an influencer.
These usually take the form of questions that focus
on the degree to which a sample is similar to a
population. Their similarity will be based on the
dependent variable, but no influencer will be
present.

106. Quick note – there will be some research questions
that only have a dependent variable (the thing
being influenced) without an influencer.
These usually take the form of questions that focus
on the degree to which a sample is similar to a
population. Their similarity will be based on the
dependent variable, but no influencer will be
present.

107. Quick note – there will be some research questions
that only have a dependent variable (the thing
being influenced) without an influencer.
These usually take the form of questions that focus
on the degree to which a sample is similar to a
population. Their similarity will be based on the
dependent variable, but no influencer will be
present.

108. Here is an example:

109. A random sample of 22 fifth grade pupils have a
grade point average of 3.6.

110. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4.

111. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?

112. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?
In this case, the dependent variable is GPA. This type of
analysis is generally a preliminary step. If the sample GPA is
shown to be representative of the population GPA, then
studies showing the impact of some influencer (e.g., study
habits, instructional software) are then conducted.

113. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?
In this case, the dependent variable is GPA. This type of
analysis is generally a preliminary step. If the sample GPA is
shown to be representative of the population GPA, then
studies showing the impact of some influencer (e.g., study
habits, instructional software) are then conducted.

114. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?
In this case, the dependent variable is GPA. This type of
analysis is generally a preliminary step. If the sample GPA
is shown to be representative of the population GPA, then
studies showing the impact of some influencer (e.g., study
habits, instructional software) are then conducted.

115. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?
In this case, the dependent variable is GPA. This type of
analysis is generally a preliminary step. If the sample GPA is
shown to be representative of the population GPA, then
studies showing the impact of some influencer (e.g., study
habits, instructional software) are then conducted.

116. A random sample of 22 fifth grade pupils have a
grade point average of 3.6. The grade point
average (GPA) of all fifth grade pupils of the last
five years is 3.4. Is the GPA of the 22 pupils
significantly different from the populations’
GPA?
In this case, the dependent variable is GPA. This type of
analysis is generally a preliminary step. If the sample GPA is
shown to be representative of the population GPA, then
studies showing the impact of some influencer (e.g., study
habits, instructional software) are then conducted.

117. Note – the majority of the problems in this
course will not be like this, but in case you run
into the few that are, hopefully this last bit of
instruction will be helpful to you.

118. Now, determine the number of dependent
variables in the problem you are working on.
1 Dependent Variable
2+ Dependent Variables