measurement scales (1)
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Scales of Measurement
Learning Module
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
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
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
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
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
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
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 8 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 9 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 10 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 11 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 12 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 13 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50OF. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 14 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50OF. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 15 of 85
The four common scales of measurement are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50OF. . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 16 of 85
Nominal, Ordinal, Interval, Ratio
Slide 17 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
Slide 18 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
1 = American
Slide 19 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
1 = American
2 = Canadian
Slide 20 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
1 = American
2 = Canadian
3 = Mexican
Slide 21 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 22 of 85
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
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
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
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
Nominal, Ordinal, Interval, Ratio
The root of the term “nominal” is “nom” meaning “name”.
Slide 27 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
Slide 28 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
1 = American
2 = Canadian
Slide 29 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
1 is not more than 2 and2 is not less than 1 in this context
1 = American
2 = Canadian
Slide 30 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval
Slide 31 of 85
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 = American2 = Canadian3 = Mexican
Slide 32 of 85
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
Nominal, Ordinal, Interval, Ratio
Nominal scales
• assume no quantity of the attribute.
• has no particular interval.
• has no zero or starting point.1 = American2 = Canadian3 = Mexican
Slide 34 of 85
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 = American2 = Canadian3 = Mexican
Slide 35 of 85
Nominal, Ordinal, Interval, Ratio
Slide 36 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Slide 37 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Private1
Corporal2
Sargent3
Lieutenant4
Major5
Colonel6
General7
Slide 38 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Private1
Corporal2
Sargent3
Lieutenant4
Major5
Colonel6
General7
Slide 39 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Slide 41 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
3rd
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd)Slide 42 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
3rd
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd)Slide 43 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
Slide 44 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
Lieutenant4
Colonel6
A colonel has more authority than a Lieutenant
Slide 45 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
1st place is higher than 3rd place
3rd
Place1st
Place
Slide 46 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
Slide 47 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
3rd
Place15’ 2”
2nd
Place16’ 1”
Slide 48 of 85
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
Place15’ 2”
2nd
Place16’ 1”
Slide 49 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales
• assume quantity of the attribute.
• do not have equal intervals.
3rd
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
Slide 50 of 85
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
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
Slide 51 of 85
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
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
A higher number only
represents more of the attribute
than a lower number,
Slide 52 of 85
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
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
. . . but how much more is
undefined.
Slide 53 of 85
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
Place15’ 2”
2nd
Place16’ 1”
1st
Place16’ 3”
The difference between points
on the scale varies from
point to point
Slide 54 of 85
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
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
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
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
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
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
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
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
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
Important Point
Slide 64 of 85
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
Interesting Note
Slide 66 of 85
Interesting Note
Technically, numbers on an ordinal scale cannot be added or subtracted.
Slide 67 of 85
Interesting Note
Technically, numbers on an ordinal scale cannot be added or subtracted.
(but we frequently do it anyway !)
Slide 68 of 85
Ordinal Numbers in a Data Set
Slide 69 of 85
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
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
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
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
Nominal, Ordinal, Interval, Ratio
Slide 74 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
Slide 75 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
Temperature
Slide 76 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
Slide 77 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
Slide 78 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales
• assume quantity of the attribute.
• have equal intervals.
40o - 41o
100o - 101o
70o - 71o
Slide 79 of 85
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
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
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 0o F
Slide 82 of 85
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 0o F
That has an arbitrary feel to it.
Doesn’t it? Slide 83 of 85
Technically, numbers on an interval scale can be added and subtracted
Slide 84 of 85
Technically, numbers on an interval scale can be added and subtracted
70o
Slide 85 of 85
Technically, numbers on an interval scale can be added and subtracted
100o
70o
Slide 86 of 85
Technically, numbers on an interval scale can be added and subtracted
100o
70o
100o is 30o more (+) than 70o
Slide 87 of 85
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
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
Slide 89 of 85
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
100o
50o
Slide 90 of 85
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
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
Interval Numbers in a Data Set
Slide 93 of 85
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
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
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
Nominal, Ordinal, Interval, Ratio
Slide 97 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
Slide 98 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales
• assume quantity of the attribute.
Slide 99 of 85
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
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
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
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
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
Ratio Numbers in a Data Set
Slide 105 of 85
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
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
Important Point
Slide 108 of 85
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
Important Point
Numbers on a ratio scale
• carry more information than the same numbers on an interval or ordinal scale.
Slide 110 of 85
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
Two more Important Points
Slide 112 of 85
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
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
Let’s Review
1. Which scale does not measure quantity or amount?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 115 of 85
Let’s Review
1. Which scale does not measure quantity or amount?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 116 of 85
Let’s Review
2. Which scale has a zero or starting point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 117 of 85
Let’s Review
2. Which scale has a zero or starting point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Slide 118 of 85
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
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
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
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
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
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
Let’s Review
6. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
Let’s Review
6. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
Let’s Review
7. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
Let’s Review
7. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
Let’s Review
8. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
Let’s Review
8. Which scale is represented by the highlighted column in the data set?
A. Nominal
B. Ordinal
C. Interval
D. RatioStudent 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
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
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
Let’s Review
10. Under which scale would you classify a Likertscale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
O Strongly DisagreeO DisagreeO Slightly DisagreeO Slightly AgreeO Strongly Disagree.
Slide 133 of 85
Let’s Review
10. Under which scale would you classify a Likertscale?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
O Strongly DisagreeO DisagreeO Slightly DisagreeO Slightly AgreeO Strongly Disagree.
Slide 134 of 85
Let’s Review
11. Under which scale would you classify social security numbers?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
987-65-4321
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Let’s Review
11. Under which scale would you classify social security numbers?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
987-65-4321
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Let’s Review
12. Under which scale would you classify
the College Football Top 25 ranking?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
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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
Let’s Review
12. Under which scale would you classify
the College Football Top 25 ranking?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
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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
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 depression2. 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
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 depression2. 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
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
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
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 body2. 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
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 body2. 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
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
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
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
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
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
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:
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
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
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
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