How many variables are there?

1. How many variables are there?

2. This presentation is designed to help you
identify the number of variables in your
relationship-oriented question.

3. Here are your options:

4. Here are your options:
2 variables
or
3 or more varaiables

5. What is a variable?

6. A variable is something that can vary or change.

7. First a variable is something that can vary or change.
For example, temperature varies from day to day.

8. First a variable is something that can vary or changes.
For example, temperature varies from day to day.
Ice cream sales can vary from day to day.

9. First a variable is something that can vary or changes.
For example, temperature varies from day to day.
Ice cream sales can vary from day to day.
Religious affiliation (eg., Catholic, Protestant, Jew,
Mormon, Muslim) can vary from person to person.

10. First a variable is something that can vary or changes.
For example, temperature varies from day to day.
Ice cream sales can vary from day to day.
Religious affiliation (eg., Catholic, Protestant, Jew,
Mormon, Muslim) can vary from person to person.
While gender can only vary two ways (e.g. male,
female), it sill varies from person to person and
therefore is a variable.

11. First a variable is something that can vary or changes.
For example, temperature varies from day to day.
Ice cream sales can vary from day to day.
Religious affiliation (eg., Catholic, Protestant, Jew,
Mormon, Muslim) can vary from person to person.
While gender can only vary two ways (e.g. male,
female), it sill varies from person to person and
therefore is a variable.

12. In a relationship question there are generally two
variables whose relationship is under investigation.

13. For example:

14. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.

15. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
One variable

16. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
This variable
could take on
a whole range
of values

17. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as

18. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as 1-10 grams

19. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as 1-10 grams
Soccer
Player
Vitamin
B Grams
A 9
B 1
C 3
D 2
E 10

20. Or the variable can take on another set of values.

21. 1 = No vitamin B
2 = Some vitamin B
3 = A lot of vitamin B

22. 1 = No vitamin B
2 = Some vitamin B
3 = A lot of vitamin B
Soccer
Player
Amount
of Vit B
A
B
C
D
E

23. 1 = No vitamin B
2 = Some vitamin B
3 = A lot of vitamin B
Soccer
Player
Amount
of Vit B
A 3
B 1
C 2
D 3
E 2

24. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
This 2nd variable
could take on a
whole range of
values as well.

25. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as

26. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as
0 cramps per game
1 cramps per game
2 cramps per game
3 cramps per game, etc.

27. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as
0 cramps per game
1 cramps per game
2 cramps per game
3 cramps per game, etc.
Soccer
Player
Amount
of Vit B
A 3
B 1
C 2
D 3
E 2

28. Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
such as
0 cramps per game
1 cramps per game
2 cramps per game
3 cramps per game, etc.
Soccer
Player
Amount
of Vit B
Cramps
Per Game
A 3 0
B 1 4
C 2 2
D 3 1
E 2 2

29. Therefore:

30. This was an example of a word problem with two
variables:

31. This was an example of a word problem with two
variables:
Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.

32. This was an example of a word problem with two
variables:
Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
Soccer
Player
Amount
of Vit B
Cramps
Per Game
A 3 0
B 1 4
C 2 2
D 3 1
E 2 2

33. This was an example of a word problem with two
variables:
Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
1st variable
Soccer
Player
Amount
of Vit B
Cramps
Per Game
A 3 0
B 1 4
C 2 2
D 3 1
E 2 2

34. This was an example of a word problem with two
variables:
Researchers wish to determine the relationship
between vitamin B intake and soccer player cramping.
Soccer
Player
Amount
of Vit B
2nd variable
Cramps
Per Game
A 3 0
B 1 4
C 2 2
D 3 1
E 2 2

35. Here is another example:

36. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.

37. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.

38. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
1st variable –
Grade Level
1 = 3rd graders
2 = 4th graders

39. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
1st variable –
Grade Level
1 = 3rd graders
2 = 4th graders

40. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.

41. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
2nd variable –
bullying
Incidents of
Bullying per
week (1, 2, 3,
4, etc.)

42. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
2nd variable –
bullying
Incidents of
bullying per
week (1, 2, 3,
4, etc.)

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

44. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.

45. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.

46. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
School Grade
1 = 3rd
2 = 4th
Incidents
of
Bullying
A
B
C
D
E

47. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
School Grade
1 = 3rd
2 = 4th
Incidents
of
Bullying
A 1
B 2
C 1
D 1
E 2

48. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
School Grade
1 = 3rd
2 = 4th
Incidents
of
Bullying
A 1
B 2
C 1
D 1
E 2

49. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
School Grade
1 = 3rd
2 = 4th
Incidents
of
Bullying
A 1 5
B 2 2
C 1 6
D 1 7
E 2 1

50. You have been asked to see if third graders tend to
bully fellow class mates more than fourth graders
across 5 different schools.
Once again, there are
two variables in this problem
School Grade
1 = 3rd
2 = 4th
Incidents
of
Bullying
A 1 5
B 2 2
C 1 6
D 1 7
E 2 1

51. There are other instances when you have three or
more variables:

52. For example:

53. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.

54. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A
B
C
D
E

55. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A
B
C
D
E

56. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A
B
C
D
E

57. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2
B 3.7
C 3.1
D 2.8
E 3.9

58. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
1st Variable
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2
B 3.7
C 3.1
D 2.8
E 3.9

59. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2
B 3.7
C 3.1
D 2.8
E 3.9

60. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26
B 3.7 27
C 3.1 22
D 2.8 25
E 3.9 23

61. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
2nd Variable
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26
B 3.7 27
C 3.1 22
D 2.8 25
E 3.9 23

62. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
A 3.2 26 5
B 3.7 27 3
C 3.1 22 0
D 2.8 25 1
E 3.9 23 3

63. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26 5
B 3.7 27 3
C 3.1 22 0
D 2.8 25 1
E 3.9 23 3

64. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
3rd Variable
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26 5
B 3.7 27 3
C 3.1 22 0
D 2.8 25 1
E 3.9 23 3

65. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
A 3.2 26 5
B 3.7 27 3
C 3.1 22 0
D 2.8 25 1
E 3.9 23 3

66. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26 5 1
B 3.7 27 3 1
C 3.1 22 0 2
D 2.8 25 1 2
E 3.9 23 3 1

67. University administrators wish to know the degree to
which GPA, ACT scores, and the number of
extracurricular activities applicants participated in,
predict students being admitted into the university.
4th Variable
Applicant GPA ACT # of Extracrclr
Activities
Admitted
1 = yes, 2 = no
A 3.2 26 5 1
B 3.7 27 3 1
C 3.1 22 0 2
D 2.8 25 1 2
E 3.9 23 3 1

68. So, that is an example of a word problem with three or
more variables.

69. Note – there is one special case that you should be
aware of.

70. Some word problems will be worded as follows:

71. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.

72. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.

73. Here is the data set for this question

74. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

75. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
1st Variable
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

76. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

77. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
2nd Variable
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

78. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

79. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
Average Daily
Peanut Butter
Intake in grams
Age is actually NOT
considered a
3rd Variable
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

80. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
Participant
That is because the two variables of interest are
peanut butter intake and gender, controlling for
Average Daily
Peanut Butter
Intake in grams
age is an additional analysis.
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

81. You have been asked to determine if a relationship
exists between the amount of peanut butter consumed
and gender controlling for age.
Study
The idea of controlling for another variable will be explained in another
presentation, but it is important for you to know that a problem like this is
Participant
examining the relationship between TWO not Three variables.
Average Daily
Peanut Butter
Intake in grams
Gender
1 = male
2 = female
Age
1 = 0-25
2 = 26-45
A 6 1 1
B 3 1 2
C 2 2 1
D 4 2 2
E 2 1 1

82. Look at the problem you are working on and
determine if it contains:

83. Look at the problem you are working on and
determine if it contains:
2 variables
or
3 or more varaiables