The document discusses different scales of measurement used in research. There are four main scales: nominal, ordinal, interval, and ratio. Nominal scales use numbers to replace categories or names and assume no quantitative relationship between numbers. Ordinal scales represent relative quantities of attributes but intervals between numbers are not equal. Interval and ratio scales both assume equal intervals but ratio scales have a true zero point.

1. Scales of Measurement
Learning Module

2. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and carry different information and symbolize
different phenomena across scales (i.e., 1 =
Catholic, 2 = Mormon . . . or 1 = Agree, 2 =
Disagree, or 1 = correct, 0 = incorrect)
Slide 2 of 85

3. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and carry different information and symbolize
different phenomena across scales (i.e., 1 =
Catholic, 2 = Mormon . . . or 1 = Agree, 2 =
Disagree, or 1 = correct, 0 = incorrect)
Slide 3 of 85

4. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and symbolize different phenomena across
scales (i.e., 1 = Catholic, 2 = Mormon . . . or 1 =
Agree, 2 = Disagree, or 1 = correct, 0 = incorrect)
Slide 4 of 85

5. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and symbolize different phenomena across
scales (i.e.,
• 1 = Catholic, 2 = Mormon . . .
• 1 = Agree, 2 = Disagree
• 1 = correct, 0 = incorrect
Slide 5 of 85

6. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and symbolize different phenomena across
scales (i.e.,
• 1 = Catholic, 2 = Mormon . . .
• 1 = Agree, 2 = Disagree
• 1 = correct, 0 = incorrect
Slide 6 of 85

7. Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and symbolize different phenomena across
scales (i.e.,
• 1 = Catholic, 2 = Mormon . . .
• 1 = Agree, 2 = Disagree
• 1 = correct, 0 = incorrect
Slide 7 of 85

8. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 8 of 85

9. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 9 of 85

10. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 10 of 85

11. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 11 of 85

12. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 12 of 85

13. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 13 of 85

14. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
F. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 14 of 85

15. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
F. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 15 of 85

16. The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30O
F, 40O
F, 50O
F. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 16 of 85

17. Nominal, Ordinal, Interval, Ratio
Slide 17 of 85

18. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
Slide 18 of 85

19. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
Slide 19 of 85

20. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
Slide 20 of 85

21. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Slide 21 of 85

22. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 22 of 85

23. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Student Nationality Test Scores
1 3 32
2 1 28
3 3 33
4 2 27
5 1 34
6 2 31
Data Set
Slide 23 of 85

24. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Student Nationality Test Scores
1 3 32
2 1 28
3 3 33
4 2 27
5 1 34
6 2 31
Data Set
Slide 24 of 85

25. Nominal
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Student Nationality Test Scores
1 3 32
2 1 28
3 3 33
4 2 27
5 1 34
6 2 31
Data Set
Slide 25 of 85

26. Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for
names.
1 = American
2 = Canadian
3 = Mexican
Student Nationality Test Scores
1 3 32
2 1 28
3 3 33
4 2 27
5 1 34
6 2 31
Data Set
Slide 26 of 85

27. Nominal, Ordinal, Interval, Ratio
The root of the term “nominal” is “nom”
meaning “name”.
Slide 27 of 85

28. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
Slide 28 of 85

29. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
1 = American
2 = Canadian
Slide 29 of 85

30. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
1 is not more than 2 and
2 is not less than 1 in this context
1 = American
2 = Canadian
Slide 30 of 85

31. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval
Slide 31 of 85

32. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval
1 and 2 and 3 are not equal intervals because
there is no quantity involved.
1 = American
2 = Canadian
3 = Mexican
Slide 32 of 85

33. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval.
• has no zero or starting point.
Slide 33 of 85

34. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval.
• has no zero or starting point.
1 = American
2 = Canadian
3 = Mexican
Slide 34 of 85

35. Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval.
• has no zero or starting point.
Because there is no quantity involved there is
no such thing as a zero point (ie., complete
absence of nationality).
1 = American
2 = Canadian
3 = Mexican
Slide 35 of 85

36. Nominal, Ordinal, Interval, Ratio
Slide 36 of 85

37. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
Slide 37 of 85

38. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
Private
1
Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Slide 38 of 85

39. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
Private
1
Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Slide 39 of 85

40. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.

41. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
Slide 41 of 85

42. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 42 of 85

43. Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent
relative amounts of an attribute.
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 43 of 85

44. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
Slide 44 of 85

45. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
Lieutenant
4
Colonel
6
A colonel has more authority than a Lieutenant
Slide 45 of 85

46. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
1st place is higher than 3rd place
3rd
Place
1st
Place
Slide 46 of 85

47. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
Slide 47 of 85

48. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
3rd
Place
15’ 2”
2nd
Place
16’ 1”
Slide 48 of 85

49. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the
same interval as the distance between 2nd and 1st place (1”)
3rd
Place
15’ 2”
2nd
Place
16’ 1”
Slide 49 of 85

50. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Slide 50 of 85

51. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the
same interval as the distance between 2nd and 1st place (1”)
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Slide 51 of 85

52. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the
same interval as the distance between 2nd and 1st place (1”)
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
A higher
number only
represents more
of the attribute
than a lower
number,
Slide 52 of 85

53. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the
same interval as the distance between 2nd and 1st place (1”)
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
. . . but how
much more is
undefined.
Slide 53 of 85

54. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the
same interval as the distance between 2nd and 1st place (1”)
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
The difference
between points
on the scale
varies from
point to point
Slide 54 of 85

55. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
Slide 55 of 85

56. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Completely Disagree
O Mostly Disagree
O Mostly Agree
O Completely Agree
Slide 56 of 85

57. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Completely Disagree
O Mostly Disagree
O Mostly Agree
O Completely Agree
Slide 57 of 85

58. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
Slide 58 of 85

59. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Not at All
O Very Little
O Somewhat
O Quite a Bit
Slide 59 of 85

60. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Not at All
O Very Little
O Somewhat
O Quite a Bit
Slide 60 of 85

61. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
Slide 61 of 85

62. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Not Important
O Slightly Important
O Somewhat Important
O Very Important
Slide 62 of 85

63. Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
• may have an arbitrary zero or starting point.
O Not Important
O Slightly Important
O Somewhat Important
O Very Important
Slide 63 of 85

64. Important Point
Slide 64 of 85

65. Important Point
Numbers on an ordinal scale are limited in the
information they carry (i.e., no equal intervals,
no zero point)
Slide 65 of 85

66. Interesting Note
Slide 66 of 85

67. Interesting Note
Technically, numbers on an ordinal scale cannot
be added or subtracted.
Slide 67 of 85

68. Interesting Note
Technically, numbers on an ordinal scale cannot
be added or subtracted.
(but we frequently do it anyway !)
Slide 68 of 85

69. Ordinal Numbers in a Data Set
Slide 69 of 85

70. Ordinal Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
Slide 70 of 85

71. Ordinal Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
Slide 71 of 85

72. Ordinal Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
Nominal
Slide 72 of 85

73. Ordinal Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
OrdinalNominal
Slide 73 of 85

74. Nominal, Ordinal, Interval, Ratio
Slide 74 of 85

75. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
Slide 75 of 85

76. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
Temperature
Slide 76 of 85

77. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
Slide 77 of 85

78. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
Slide 78 of 85

79. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
40o - 41o
100o - 101o
70o - 71o
Slide 79 of 85

80. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
40o - 41o
100o - 101o
70o - 71o
Each set of readings are the same
distance apart: 1o
Slide 80 of 85

81. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
• may have an arbitrary zero or starting point.
Slide 81 of 85

82. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
• may have an arbitrary zero or starting point.
Daniel Gabriel Fahrenheit (1686–1736)
determined that equal amounts of ice,
water, and salt mixed together reached a
stable temperature at 0
o
F
Slide 82 of 85

83. Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
• may have an arbitrary zero or starting point.
Daniel Gabriel Fahrenheit (1686–1736)
determined that equal amounts of ice,
water, and salt mixed together reached a
stable temperature at 0
o
F
That has an
arbitrary feel to it.
Doesn’t it? Slide 83 of 85

84. Technically, numbers on an interval scale can be
added and subtracted
Slide 84 of 85

85. Technically, numbers on an interval scale can be
added and subtracted
70o
Slide 85 of 85

86. Technically, numbers on an interval scale can be
added and subtracted
100o
70o
Slide 86 of 85

87. Technically, numbers on an interval scale can be
added and subtracted
100o
70o
100o is 30o more (+) than 70o
Slide 87 of 85

88. Technically, numbers on an interval scale can be
added and subtracted
100o
70o
100o is 30o more (+) than 70o
70o is 30o less (-) than 100o
Slide 88 of 85

89. Technically, numbers on an interval scale can be
added and subtracted but not divided and
multiplied.
Slide 89 of 85

90. Technically, numbers on an interval scale can be
added and subtracted but not divided and
multiplied.
100o
50o
Slide 90 of 85

91. Technically, numbers on an interval scale can be
added and subtracted but not divided and
multiplied.
100o
50oAnd 50o is NOT half (/) as hot as 100o
100o is NOT twice (x) as hot as 50o
Slide 91 of 85

92. Technically, numbers on an interval scale can be
added and subtracted but not divided and
multiplied.
100o
50oAnd 50o is NOT half (/) as hot as 100o
But 100o is NOT twice (x) as hot as 50o
But many do so
anyways 
Slide 92 of 85

93. Interval Numbers in a Data Set
Slide 93 of 85

94. Interval Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
Slide 94 of 85

95. Interval Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
OrdinalNominal Interval
Slide 95 of 85

96. Interval Numbers in a Data Set
Student Nationality Place Test Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Data Set
OrdinalNominal Interval
Slide 96 of 85

97. Nominal, Ordinal, Interval, Ratio
Slide 97 of 85

98. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
Slide 98 of 85

99. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
Slide 99 of 85

100. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
Slide 100 of 85

101. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
• have equal intervals.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
Slide 101 of 85

102. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
• have equal intervals.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
Every inch represents a unit of measure that is the
same across all inches Slide 102 of 85

103. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
• have equal intervals.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
With the interval nature of the data, you can say that player 4
(blue team) is 6 inches taller than Player 19 (yellow team)Slide 103 of 85

104. Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
• have equal intervals.
• has a zero or starting point.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
With a zero starting point (0’0”) you can say that player
6 (blue team) is 4/5 the size of player 4 (blue team)Slide 104 of 85

105. Ratio Numbers in a Data Set
Slide 105 of 85

106. Ratio Numbers in a Data Set
Student Nationality Place Test Scores Height
1 3 3 32 5’2”
2 1 5 28 6’3”
3 3 2 33 6’0”
4 2 6 27 5’8”
5 1 1 34 6’1”
6 2 4 31 5’5”
Data Set
OrdinalNominal Interval
Slide 106 of 85

107. Ratio Numbers in a Data Set
Student Nationality Place Test Scores Height
1 3 3 32 5’2”
2 1 5 28 6’3”
3 3 2 33 6’0”
4 2 6 27 5’8”
5 1 1 34 6’1”
6 2 4 31 5’5”
Data Set
OrdinalNominal Interval Ratio
Slide 107 of 85

108. Important Point
Slide 108 of 85

109. Important Point
Numbers on a ratio scale
• carry more information than the same
numbers on an interval or ordinal scale.
• can be
– added,
– subtracted,
– multiplied, or
– divided.
Slide 109 of 85

110. Important Point
Numbers on a ratio scale
• carry more information than the same
numbers on an interval or ordinal scale.
Slide 110 of 85

111. Important Point
Numbers on a ratio scale
• carry more information than the same
numbers on an interval or ordinal scale.
• can be
– added,
– subtracted,
– multiplied, or
– divided.
Slide 111 of 85

112. Two more Important Points
Slide 112 of 85

113. Two more Important Points
1. More adequate scales can be easily
converted to less adequate scales.
2. Most statistical programs will treat interval
and ratio data the same.
Ratio - - - > Interval - - - > Ordinal - - - > Nominal
Slide 113 of 85

114. Two more Important Points
1. More adequate scales can be easily
converted to less adequate scales.
2. Most statistical programs will treat interval
and ratio data the same.
Ratio - - - > Interval - - - > Ordinal - - - > Nominal
Slide 114 of 85

115. Let’s Review
1. Which scale does not measure quantity or
amount?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 115 of 85

116. Let’s Review
1. Which scale does not measure quantity or
amount?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 116 of 85

117. Let’s Review
2. Which scale has a zero or starting point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 117 of 85

118. Let’s Review
2. Which scale has a zero or starting point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 118 of 85

119. Let’s Review
3. Which scale captures amount but does not
have equal distances between units of measure?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 119 of 85

120. Let’s Review
3. Which scale captures amount but does not
have equal distances between units of measure?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 120 of 85

121. Let’s Review
4. Which scale has equal distance between
adjacent points but no zero point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 121 of 85

122. Let’s Review
4. Which scale has equal distance between
adjacent points but no zero point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 122 of 85

123. Let’s Review
5. Which scale expresses more of an attribute
across the scale, but does not express the
distance between each point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 123 of 85

124. Let’s Review
5. Which scale expresses more of an attribute
across the scale, but does not express the
distance between each point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 124 of 85

125. Let’s Review
6. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 125 of 85

126. Let’s Review
6. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 126 of 85

127. Let’s Review
7. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 127 of 85

128. Let’s Review
7. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 128 of 85

129. Let’s Review
8. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 129 of 85

130. Let’s Review
8. Which scale is represented by the highlighted
column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Student Test Scores Place Nationality Height
1 32 3 3 5’2”
2 28 5 1 6’3”
3 33 2 3 6’0”
4 27 6 2 5’8”
5 34 1 1 6’1”
6 31 4 2 5’5”Slide 130 of 85

131. Let’s Review
9. Under which scale would you classify the
Kelvin scale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
What is the Kelvin Scale?
The Kelvin scale assumes quantity of
heat and has equal intervals along
the scale with an absolute zero
Absolute zero heat represents zero
molecular motion and is a good
starting point for measurement.
Slide 131 of 85

132. Let’s Review
9. Under which scale would you classify the
Kelvin scale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
What is the Kelvin Scale?
The Kelvin scale assumes quantity of
heat and has equal intervals along
the scale with an absolute zero
Absolute zero heat represents zero
molecular motion and is a good
starting point for measurement.
Slide 132 of 85

133. Let’s Review
10. Under which scale would you classify a Likert
scale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
O Strongly Disagree
O Disagree
O Slightly Disagree
O Slightly Agree
O Strongly Disagree.
Slide 133 of 85

134. Let’s Review
10. Under which scale would you classify a Likert
scale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
O Strongly Disagree
O Disagree
O Slightly Disagree
O Slightly Agree
O Strongly Disagree.
Slide 134 of 85

135. Let’s Review
11. Under which scale would you classify social
security numbers?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
987-65-4321
Slide 135 of 85

136. Let’s Review
11. Under which scale would you classify social
security numbers?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
987-65-4321
Slide 136 of 85

137. Let’s Review
12. Under which scale would you classify
the College Football Top 25 ranking?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 137 of 85

138. Let’s Review
12. Under which scale would you classify
the College Football Top 25 ranking?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 138 of 85

139. Let’s Review
12. Under which scale would you classify
the College Football Top 25 ranking?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 139 of 85

140. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
? Yes Yes Absolute Add, subtract,
multiply, divide
Yes Yes Arbitrary Add, subtract
Yes No Arbitrary None
No No Irrelevant None
Slide 140 of 85

141. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
Yes Yes Arbitrary Add, subtract
Yes No Arbitrary None
No No Irrelevant None
Slide 141 of 85

142. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
? Yes Yes Arbitrary Add, subtract
Yes No Arbitrary None
No No Irrelevant None
Slide 142 of 85

143. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
Interval Yes Yes Arbitrary Add, subtract
? Yes No Arbitrary None
No No Irrelevant None
Slide 143 of 85

144. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
Interval Yes Yes Arbitrary Add, subtract
Ordinal Yes No Arbitrary None
No No Irrelevant None
Slide 144 of 85

145. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
Interval Yes Yes Arbitrary Add, subtract
Ordinal Yes No Arbitrary None
? No No Irrelevant None
Slide 145 of 85

146. 13. What scale is represented in each row?
Scale Quantity
Assumed
Equal Intervals Zero Point Calculations
Ratio Yes Yes Absolute Add, subtract,
multiply, divide
Interval Yes Yes Arbitrary Add, subtract
Ordinal Yes No Arbitrary None
Nominal No No Irrelevant None
Slide 146 of 85

147. More Practice Problems
What type of data is represented in this problem?
A. Nominal? If yes, what is it?
___________________
B. Ordinal? If yes, what is it?
___________________
C. Interval? If yes, what is it?
___________________
D. Ratio? If yes, what is it? ___________________
Slide 147 of 85

148. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Slide 148 of 85

149. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Slide 149 of 85

150. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Ethnic Group
Slide 150 of 85

151. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Ethnic Group
Level of public religious devotion
Slide 151 of 85

152. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Ethnic Group
Level of public religious devotion
Slide 152 of 85
None

153. More Practice Problems
14. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Ethnic Group
Level of public religious devotion
None
Length of hair
Slide 153 of 85

154. More Practice Problems
15. Suppose a researcher wants to analyze whether
different ethnic groups vary in terms of their level of
public religious devotion. She also thinks that there
might be a relationship between public religious devotion
and the length of hair for both men and women.
What type of data is represented in this problem?
A. Nominal? If yes, what is it? ___________________
B. Ordinal? If yes, what is it? ___________________
C. Interval? If yes, what is it? ___________________
D. Ratio? If yes, what is it? ___________________
Ethnic Group
Level of public religious devotion
None
Length of hair
Slide 154 of 85
Gender

155. More Practice Problems
16. Which data type is represented in the scenario below:
A researcher created an assessment of depression that
included ten T/F questions. Subjects were given 1 point for
every question that they answered correctly. Scores could
range from 0 to 10.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 155 of 85

156. More Practice Problems
16. Which data type is represented in the scenario below:
A researcher created an assessment of depression that
included ten T/F questions. Subjects were given 1 point for
every question that they answered correctly. Scores could
range from 0 to 10.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 156 of 85

157. More Practice Problems
16. Which data type is represented in the scenario below:
A researcher created an assessment of depression that
included ten T/F questions. Subjects were given 1 point for
every question that they answered correctly. Scores could
range from 0 to 10.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
1. higher scores represent more depression
2. the difference between 10 and 9 is the same as the
difference between 9 and 8.
3. a score of 0 is an arbitrary starting point based on the
limited number of questions selected by the researcher.
It is probable that there is some degree of depression in
subjects that score 0.
Slide 157 of 85

158. More Practice Problems
16. Which data type is represented in the scenario below:
A researcher created an assessment of depression that
included ten T/F questions. Subjects were given 1 point for
every question that they answered correctly. Scores could
range from 0 to 10.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
1. higher scores represent more depression
2. the difference between 10 and 9 is the same as the
difference between 9 and 8.
3. a score of 0 is an arbitrary starting point based on the
limited number of questions selected by the researcher.
It is probable that there is some degree of depression in
subjects that score 0.
In many cases, this can be a subjective determination. In this case, it
can be argued that this is actually an ordinal scale because different
questions might carry different predictive weight. For example “I feel
suicidal” might be more indicative of depression than “I feel blue
more days than not”.
Slide 158 of 85

159. More Practice Problems
17. Which data type is represented in the scenario below:
A researcher believes that the number of broken bones that
someone suffers can be counted as discrete trauma. She
includes an item in her survey that reads “How many bones
have you broken in your life time?”
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 159 of 85

160. More Practice Problems
17. Which data type is represented in the scenario below:
A researcher believes that the number of broken bones that
someone suffers can be counted as discrete trauma. She
includes an item in her survey that reads “How many bones
have you broken in your life time?”
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 160 of 85

161. More Practice Problems
17. Which data type is represented in the scenario below:
A researcher believes that the number of broken bones that
someone suffers can be counted as discrete trauma. She
includes an item in her survey that reads “How many bones
have you broken in your life time?”
A. Nominal
B. Ordinal
C. Interval
D. Ratio
1. higher scores represent more trauma to the body
2. the difference between 3 bones and 2 bones is the same
as the difference between 2 bones and 1 bone.
3. the starting point, zero broken bones, is an absolute zero.
Zero broken bones is really zero broken bones.
Slide 161 of 85

162. More Practice Problems
17. Which data type is represented in the scenario below:
A researcher believes that the number of broken bones that
someone suffers can be counted as discrete trauma. She
includes an item in her survey that reads “How many bones
have you broken in your life time?”
A. Nominal
B. Ordinal
C. Interval
D. Ratio
1. higher scores represent more trauma to the body
2. the difference between 3 bones and 2 bones is the same
as the difference between 2 bones and 1 bone.
3. the starting point, zero broken bones, is an absolute zero.
Zero broken bones is really zero broken bones.
Once again, technically this can be categorized as an ordinal
scale, because if most of your broken bones occurred when
you were two years old, that might be less traumatic to the
body than if they occurred at age 90.
Slide 162 of 85

163. More Practice Problems
17. Which data type is represented in the scenario below:
A researcher believes that the number of broken bones that
someone suffers can be counted as discrete trauma. She
includes an item in her survey that reads “How many bones
have you broken in your life time?”
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Obviously higher scores represent more trauma to the body.
The difference between 3 bones and 2 bones is the same as
the difference between 2 bones and 1 bone. The starting
point, zero broken bones, is an absolute zero. Zero broken
bones is really zero broken bones.
Once again, technically this can be categorized as an ordinal
scale, because if most of my broken bones occurred when I
was two years old, that might be less traumatic to the body
than if they occurred at age 90.
While we categorize scales as interval and ratio there could
always be some technical reason or rationale for reclassify
them as ordinal.
The degree of technicality depends on your audience and the
purposes of your research.
Slide 163 of 85

164. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
Slide 164 of 85

165. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
Is there an
assumption
of quantity?
Slide 165 of 85

166. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
NOMINAL
no
Is there an
assumption
of quantity?
Slide 166 of 85

167. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
NOMINAL
yes no
Is there an
assumption
of quantity?
Are there
equal
intervals?
Slide 167 of 85

168. In Summary
NOMINAL
ORDINAL
yes no
no
Is there an
assumption
of quantity?
Are there
equal
intervals?
Slide 168 of 85
Here is a basic decision tree that may be useful in
determining the type of data you are working with:

169. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
NOMINAL
ORDINAL
yes
yes
no
no
Is there an
assumption
of quantity?
Are there
equal
intervals?
Is there an
absolute
zero?
Slide 169 of 85

170. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
NOMINAL
ORDINAL
INTERVAL
yes
yes
no
no
no
Is there an
assumption
of quantity?
Are there
equal
intervals?
Is there an
absolute
zero?
Slide 170 of 85

171. In Summary
Here is a basic decision tree that may be useful in
determining the type of data you are working with:
NOMINAL
ORDINAL
INTERVALRATIO
yes
yes
yes
no
no
no
Is there an
assumption
of quantity?
Are there
equal
intervals?
Is there an
absolute
zero?
Slide 171 of 85