knowledge about nominal, ordinal, interval and ratio scale

1. Levels of
measurment

2. SCALE OF MEASUREMENT
 Measurement is the process of assigning numbers
or labels to objects, persons, states, or events
accordance with specific rules to represent
quantities or qualities of attributes.
in
 We do not measure specific objects, persons, etc.,
we measure attributes or features that define them.
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3. Nominal
Types of
Measurement
Scales
Ordinal Ratio
Interval 10

4. There must be distinct classes but these classes
have no quantitative properties. Therefore, no
comparison can be made in terms of one category
being higher than the other.
For example - there are two classes for the
variable gender - males and females. There are
no quantitative properties for this variable or
these classes and, therefore, gender is a nominal
variable.
Male: 1, Female: 0
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5. Nominal Level Data
• Numbers are used to classify or categorize
Example: Employment Classification
– 1 for Educator
– 2 for Construction Worker
– 3 for Manufacturing Worker
Example: Ethnicity
– 1 for Bhramin
– 2 for Chettri
– 3 for Janajati
– 4 for dalits

6. CONT…NOMINAL SCALE
Sometimes numbers are
category membership-
used to designate
Example:
Country of Origin
1 = United States
2 = Mexico
3 = Canada
4 = Other
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RDh@ker,Lecturer,PCNMS

7. Ordinal Scales
There are distinct classes but these classes have a
natural ordering or ranking. The differences can be
ordered on the basis of magnitude.
For example - final position of horses in a
thoroughbred race is an ordinal variable. The horses
finish first, second, third, fourth, and so on.
difference between first and second is not
The
necessarily equivalent to the difference between
second and third, or between third and fourth.
Qualitative measurement only
e.g. 1st , 2nd, 3rd ; excellent, good, fair, poor
Strongly agree, disagree
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8. CONT…ORDINAL SCALES
 Does not assume
are equal
that the intervals between numbers
Example:
finishing place in a race
(first place, second place)
4th place1st place 2nd place 3rd place
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

9. Ordinal Level Data
• Numbers are used to indicate rank or order
– Relative magnitude of numbers is meaningful
– Differences between numbers are not comparable
Example: Taste test ranking of three brands of soft drink
Example: Position within an organization
– 1 for President
– 2 for Vice President
– 3 for Plant Manager
– 4 for Department Supervisor
– 5 for Employee

10. Ordinal Data
Faculty and staff should receive sufficient support in imparting quality
education
1 2 3 4 5
Strongly
Agree
Agree Strongly
Disagree
DisagreeNeutral

11. INTERVAL SCALES
It is possible to compare differences in magnitude,
but importantly the zero point does not have a
natural meaning.
Designates an equal-interval ordering -
distance between, for example, a 1 and
same as the distance between a 4 and a
The
a 2 is
5
the
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Basic mathematical operation can be done

12. Interval Level Data
• Distances between consecutive integers are equal
– Relative magnitude of numbers is meaningful
– Differences between numbers are comparable
– Location of origin, zero, is arbitrary
– Vertical intercept of unit of measure transform
function is not zero
Examples: Fahrenheit Temperature, Calendar Time,

13. We can see that the same difference
exists between 10o
degree C ( 68 F)
C ( 50 F) and 20
25 C ( 77F) and 35 C ( 95 F)
But we can not say that 20C is twice as
hot as a temperature of 10C
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14. Example - Celsius temperature is an interval
is meaningful to say that 25 degrees
degrees hotter than 22 degrees Celsius,
variable. It
Celsius is 3
and that 17 degrees Celsius is the same amount
hotter (3 degrees) than 14 degrees Celsius. Notice,
however, that 0 degrees Celsius does not have a
natural meaning. That is, 0 degrees Celsius does not
mean the absence of heat!
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15. RATIO SCALES
It is the highest level for measurement
This level has all
Magnitude
the three attributes:

Equal interval
Absolute zero point
It represent continuous values
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16.  Example:
 Biophysical
Weight
parameters
Height
Volume
Blood pressure
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17. 30 Kg is thrice of 10 kg
20 cm is twice of 10 cm
8 hours is four time of 2 hours
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18. Summary
Information Nominal Ordinal Interval Ratio
Classification Yes Yes Yes Yes
Rank order Yes Yes Yes
Equal interval Yes Yes
Nonarbitrary
zero
Yes
(Source: Singleton and Straits, 2005)

19. Data Level, Operations,
and Statistical Methods
Data Level
Nominal
Ordinal
Interval
Ratio
Meaningful Operations
Classifying and Counting
All of above plus Ranking
All of above plus Addition,
Subtraction, Multiplication, and
Division
All of the above
Statistical
Methods
Nonparametric
Nonparametric
Parametric
Parametric