Scaled v. ordinal v. nominal data(3)

1. This presentation will assist you in determining if
the data associated with the problem you are
working on

2. This presentation will assist you in determining if
the data associated with the problem you are
working on
Participant Score
A 10
B 11
C 12
D 12
E 12
F 13
G 14

3. This presentation will assist you in determining if
the data associated with the problem you are
working on
Participant Score
A 10
B 11
C 12
D 12
E 12
F 13
G 14

4. This presentation will assist you in determining if
the data associated with the problem you are
working on is:

5. This presentation will assist you in determining if
the data associated with the problem you are
working on is:
Scaled

6. This presentation will assist you in determining if
the data associated with the problem you are
working on is:
Scaled
Ordinal

7. This presentation will assist you in determining if
the data associated with the problem you are
working on is:
Scaled
Ordinal
Nominal Proportional

8. Before we begin, it is important to note that with
questions of difference, where you are comparing
groups, the data you should classify as scaled,
ordinal, or nominal proportional are data that
represent RESULTS (weight gain, driving speed, IQ,
etc.),
In this case, you are NOT classifying what are called
CATEGORICAL variables like gender,
treatment/control group, type of athlete, school
type, ethnicity, political or religious affiliation, etc.

9. What is scaled data?

10. What is scaled data?
Note – scaled data has two subcategories
(1) interval data (no zero point but equal
intervals) and
(2) ratio data (a zero point and equal
intervals)

11. What is scaled data?
For the purposes of this presentation we will
not discuss these further but just focus on
both as scaled data.

12. Scaled data is data that has a couple of
attributes.

13. We will describe those attributes with
illustrations from a scaled variable:

14. We will describe those attributes with
illustrations from a scaled variable:
Temperature.

15. Attribute #1 – scaled data assume a quantity.
Meaning that 2 is more than 3 and 4 is more
than 3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.

16. Attribute #1 – scaled data assume a quantity.
Meaning that 2 is more than 3 and 4 is more
than 3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.

17. Attribute #1 – scaled data assume a quantity.
Meaning that 3is more than 2and 4 is more than
3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.

18. Attribute #1 – scaled data assume a quantity.
Meaning that 3 is more than 2 and 4is more than
3and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.

19. Attribute #1 – scaled data assume a quantity.
Meaning that 3 is more than 2 and 4 is more
than 3 and 20is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.

20. Attribute #1 – scaled data assume a quantity.
Meaning that 3 is more than 2 and 4 is more
than 3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.100 degrees is more
than 40 degrees

21. Attribute #1 – scaled data assume a quantity.
Meaning that 3 is more than 2 and 4 is more
than 3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.60 degrees is less
than 80 degrees

22. Attribute #1 – scaled data assume a quantity.
Meaning that 3 is more than 2 and 4 is more
than 3 and 20 is less than 30, etc.
For example: 40 degrees is more
than 30 degrees. 110 degrees is
less than 120 degrees.60 degrees is less
than 80 degrees
If the data represents varying
amounts then this is the first
requirement for data to be
considered - scaled.

23. Attribute #2

24. Attribute #2 – scaled data has equal intervals or each
unit has the same value.

25. Attribute #2 – scaled data has equal intervals or each
unit has the same value.
Meaning the distance between 1and 2is the same as
the distance between 14 and 15 or 1,123 and
1,124.

26. Attribute #2 – scaled data has equal intervals or each
unit has the same value.
Meaning the distance between 1and 2is the same as
the distance between 14 and 15 or 1,123 and
1,124. They all have a unit value of 1 between
them.

27. In our temperature example:

28. 40o - 41o
100o - 101o
70o – 71o
Each set of
readings are the
same distance
apart: 1o

29. 40o - 41o
100o - 101o
70o – 71o
Each set of
readings are the
same distance
apart: 1o
The point here is that each unit
value is the same across the
entire scale of numbers

30. 40o - 41o
100o - 101o
70o – 71o
Each set of
readings are the
same distance
apart: 1o
Note, this is not the case with
ordinal numbers where 1st place in
a marathon might be 2:03 hours,
2nd place 2:05 and 3rd place 2:43.
They are not equally spaced!

31. What does a scaled data set look like?

32. Here are some examples:

33. Height

34. Height
Persons Height
Carly 5’ 3”
Celeste 5’ 6”
Donald 6’ 3”
Dunbar 6’ 1”
Ernesta 5’ 4”

35. Height
Attribute #1: We are
dealing with amounts
Persons Height
Carly 5’ 3”
Celeste 5’ 6”
Donald 6’ 3”
Dunbar 6’ 1”
Ernesta 5’ 4”

36. Height
Persons Height
Carly 5’ 3”
Celeste 5’ 6”
Donald 6’ 3”
Dunbar 6’ 1”
Ernesta 5’ 4”
Attribute #2: There are equal
intervals across the scale. One inch is
the same value regardless of where
you are on the scale.

37. Intelligence Quotient (IQ)

38. Intelligence Quotient (IQ)
Persons Height IQ
Carly 5’ 3” 120
Celeste 5’ 6” 100
Donald 6’ 3” 95
Dunbar 6’ 1” 121
Ernesta 5’ 4” 103

39. Intelligence Quotient (IQ)
Persons Height IQ
Carly 5’ 3” 120
Celeste 5’ 6” 100
Donald 6’ 3” 95
Dunbar 6’ 1” 121
Ernesta 5’ 4” 103
Attribute #1: We are
dealing with amounts

40. Intelligence Quotient (IQ)
Persons Height IQ
Carly 5’ 3” 120
Celeste 5’ 6” 100
Donald 6’ 3” 95
Dunbar 6’ 1” 121
Ernesta 5’ 4” 103
Attribute #2: Supposedly there are equal
intervals across this scale. A little harder to
prove but most researchers go with it.

41. Pole Vaulting Placement

42. Pole Vaulting Placement
Persons Height IQ PVP
Carly 5’ 3” 120 3rd
Celeste 5’ 6” 100 5th
Donald 6’ 3” 95 1st
Dunbar 6’ 1” 121 4th
Ernesta 5’ 4” 103 2nd

43. Pole Vaulting Placement
Persons Height IQ PVP
Carly 5’ 3” 120 3rd
Celeste 5’ 6” 100 5th
Donald 6’ 3” 95 1st
Dunbar 6’ 1” 121 4th
Ernesta 5’ 4” 103 2nd
Attribute #1: We are
dealing with amounts

44. Pole Vaulting Placement
Persons Height IQ PVP
Carly 5’ 3” 120 3rd
Celeste 5’ 6” 100 5th
Donald 6’ 3” 95 1st
Dunbar 6’ 1” 121 4th
Ernesta 5’ 4” 103 2nd
Attribute #2: We are NOT dealing with equal
intervals. 1st place (16’0”) and 2nd place (15’8”) are
not the same distance from one another as 2nd Place
and 3rd place (12’2”).

45. Based on this explanation is your data scaled?

46. If your data is scaled as shown in these
examples, select

47. If your data is scaled as shown in these
examples, select
Scaled
Ordinal
Nominal Proportional

48. We have now demonstrated scaled data and
given you a brief introduction to ordinal data.

49. Once again, ordinal data is data that is ranked:

50. Once again, ordinal data is data that is ranked:

51. In other words,

52. Ordinal scales use numbers to represent
relative amounts of an attribute.

53. Ordinal scales use numbers to represent
relative amounts of an attribute.
1st
Place
16’ 3”

54. Ordinal scales use numbers to represent
relative amounts of an attribute.
1st
Place
16’ 3”
2nd
Place
16’ 1”

55. Ordinal scales use numbers to represent
relative amounts of an attribute.
1st
Place
16’ 3”
2nd
Place
16’ 1”
3rd
Place
15’ 2”

56. Ordinal scales use numbers to represent
relative amounts of an attribute.
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Relative Amounts of Bar Height

57. Example of relative amounts of
authority

58. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
Example of relative amounts of
authority

59. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
Notice how we are
dealing with
amounts of
authority
Example of relative amounts of
authority

60. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
But,
Example of relative amounts of
authority

61. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
But, they may not
be equally spaced.
Example of relative amounts of
authority

62. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
But, they may not
be equally spaced.
Example of relative amounts of
authority

63. Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Private
1
But, they may not
be equally spaced.
Example of relative amounts of
authority

64. You can tell if you have an ordinal data set when
the data is described as ranks.

65. You can tell if you have an ordinal data set when
the data is described as ranks.
Persons Pole Vault
Placement
Carly 3rd
Celeste 5th
Donald 1st
Dunbar 4th
Ernesta 2nd

66. Or in percentiles

67. Or in percentiles
Persons ACT
Percentile
Rank
Carly 55%
Celeste 23%
Donald 97%
Dunbar 37%
Ernesta 78%

68. If your data is ranked as shown in these
examples, select

69. If your data is ranked as shown in these
examples, select
Scaled
Ordinal
Nominal Proportional

70. Finally, let’s see what data looks like when it is
nominal proportional:

71. Nominal data is different from scaled or ordinal,

72. Nominal data is different from scaled or ordinal,
because they do not deal with amounts

73. Nominal data is different from scaled or ordinal,
because they do not deal with amounts nor
equal intervals.

74. For example,

75. Nationality is a variable that does not have
amounts nor equal intervals.

76. 1 = Canadian
2 = American

77. 1 = Canadian
2 = American
Being Canadian is not numerically or
quantitatively more than being
American

78. 1 = Canadian
2 = American
The numbers 1 and 2 do not represent
amounts. They are just a way to
distinguish the two groups numerically.

79. We could have just as easily used 1s for
Americans and 2s for Canadians

80. We could have just as easily used 1s for
Americans and 2s for Canadians
1 = Canadian
2 = American

81. We could have just as easily used 1s for
Americans and 2s for Canadians
1 = American
2 = Canadian

82. Other examples:

83. Religious Affiliation

84. Religious Affiliation
1 - Buddhist
2 - Catholic
3 - Jew
4 - Mormon
5 - Muslim
6 - Protestant

85. Gender

86. Gender
1 - Male
2 - Female

87. Preference

88. Preference:
1. People who prefer chocolate ice-cream

89. Preference:
1. People who prefer chocolate ice-cream
2. People who dislike chocolate ice-cream

90. Pass/Fail

91. Pass/Fail
1. Those who passed the test

92. Pass/Fail
1. Those who passed the test
2. Those who failed the test

93. The word “Nom” in “nominal” means “name”.

94. The word “Nom” in nominal means “name”.
Essentially we are using data to name, identify,
distinguish, classify or categorize.

95. Other names for nominal data are categorical or
frequency data.

96. Here is how the nominal data would look like in
a data set:

97. Here is how the nominal data would look like in
a data set:
Persons
Carly
Celeste
Donald
Dunbar
Ernesta

98. Here is how the nominal data would look like in
a data set:
Persons Gender
Carly
Celeste
Donald
Dunbar
Ernesta

99. Here is how the nominal data would look like in
a data set:
Persons Gender
Carly
Celeste
Donald
Dunbar
Ernesta
1 = Male
2 = Female

100. Here is how the nominal data would look like in
a data set:
Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
1 = Male
2 = Female

101. Persons Gender Preference
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2

102. Persons Gender Preference
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
1 = Like ice-cream
2 = Don’t like ice-cream

103. Persons Gender Preference
Carly 2 1
Celeste 2 1
Donald 1 1
Dunbar 1 2
Ernesta 2 2
1 = Like ice-cream
2 = Don’t like ice-cream

104. Persons Gender Preference
Carly 2 1
Celeste 2 1
Donald 1 1
Dunbar 1 2
Ernesta 2 2
Religion

105. Persons Gender Preference
Carly 2 1
Celeste 2 1
Donald 1 1
Dunbar 1 2
Ernesta 2 2
Religion
1 - Buddhist
2 - Catholic
3 - Jew
4 - Mormon
5 - Muslim
6 - Protestant

106. Persons Gender Preference
Carly 2 1
Celeste 2 1
Donald 1 1
Dunbar 1 2
Ernesta 2 2
Religion
4
2
5
6
1
1 - Buddhist
2 - Catholic
3 - Jew
4 - Mormon
5 - Muslim
6 - Protestant

107. Now that we know what nominal data is,

108. What is nominal proportional data?

109. What is nominal proportional data?
Scaled
Ordinal
Nominal Proportional

110. Nominal proportional data is simply the
proportion of individuals who are in one
category as opposed to another.

111. For example,

112. In the data set below:

113. In the data set below:
Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2

114. Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
3 out of 5 persons
are female

115. Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
Or 60% are female

116. Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
That means 2 out of 5
are male

117. Persons Gender
Carly 2
Celeste 2
Donald 1
Dunbar 1
Ernesta 2
Or 40% are male

118. In such cases you may not see a data set,

119. you may just see a question like this:

120. A claim is made that four out of five veterans (or
80%) are supportive of the current conflict.
After you sample five veterans you find that
three out of five (or 60%) are supportive. In
terms of statistical significance does this result
support or invalidate this claim?

121. If you were to put these results in a data set it
would look like this:

122. Veterans
A
B
C
D
E

123. Veterans Supportive
A
B
C
D
E

124. Veterans Supportive
A
B
C
D
E
1 = supportive
2 = not supportive

125. Veterans Supportive
A 2
B 2
C 1
D 1
E 1
1 = supportive
2 = not supportive

126. Veterans Supportive
A 2
B 2
C 1
D 1
E 1
1 = supportive
2 = not supportive
If the question is stated in terms of percentages
(e.g., 60% of veterans were supportive), then
that percentage is nominal proportional data

127. If your data is nominal proportional as shown in
these examples, select

128. If your data is nominal proportional as shown in
these examples, select
Scaled
Ordinal
Nominal Proportional

129. That concludes this explanation of scaled,
ordinal and nominal proportional data.