The process of assigning a value or
score to the observed phenomenon constitutes the process of measurement. The
rules defining the assignment of an appropriate value determine the level of measurement.
The traditional classification of level of measurement was developed by S.S.
Stevens 1946.
The four levels are-
·
Nominal level of measurement
·
Ordinal level of measurement
·
Interval level of measurement
·
Ration level of measurement
The different measurement scales are distinguished
on the basis of three important criteria-
·
Magnitude
When a scale has magnitude, one
instance of the attribute can be judged greater than, less than, or equal to
another instance of the attribute.
·
Equal intervals
Equal intervals denotes that the
magnitude of the concepts represented by unit of measurement on the scale is
equal regardless of where on the scale the unit falls.
·
Absolute Zero
An absolute zero point is a value that
indicates that nothing at all of the attribute being measured exists.
|
Level
|
Allows for
categorizing
|
Allows for
Ranking
|
Uses Equal
intervals
|
Possesses
real Zero point
|
|
Nominal
|
ok
|
|
|
|
|
Ordinal
|
ok
|
ok
|
|
|
|
Interval
|
ok
|
ok
|
ok
|
|
|
Ratio
|
ok
|
ok
|
ok
|
ok
|
Figure: Essential characteristics of
four levels of measurement
Nominal Level/scale;
Definition
The measurement scale in which numbers
are assigned to the categories or variable values for identification only is
called a nominal scale.
Properties;
·
Nominal is weakest level of measurement.
·
It doesn’t posses the attributes of
magnitude, equal intervals or an absolute zero point.
·
The data of nominal scale have no quantities
properties.
·
Of the basic postulates, the first
three pertaining to equality apply.
·
The statistical operations for this
scale are counting (frequency), % mode, and coefficient of contingency.
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.
Others
example
Player’s
jersey number, marital status, hair color etc.
Ordinal
Level/scale;
The
measurement scale in which numbers are assigned to the categories or variable
values for identification as well as ranking is called an ordinal scale.
Properties;
·
It is the 2nd weakest level of measurement.
·
It captures the properties of nominal
scale.
·
It reflects only magnitude and does not
posses the attributes of equal intervals or an absolute zero point.
·
The logical basis for rank order is to
be found in postulates 4 and 5.
·
The statistical operations for this
scale are counting, ranking, mode, medians, percentiles, coefficient of
contingency and rank order correlation.
For example;
An ordinal scale is obtained when a
group of boys is ordered from tallest to shortest.
Other examples;
Social class, economics status, pain
etc.
Interval Levels:
The measurement scale in which numbers
are assigned to the variable values in such a way that the level of measurement
is broken down on a scale of equal units and the zero value on the scale is not
absolutely zero is called an interval scale.
Properties;
·
It is the 2nd strongest level of
nominal and ordinal scales.
·
It captures the properties of nominal
and ordinal scale.
·
It posses the attributes of magnitude
and equal intervals but not an absolute zero point.
·
Most of the postulates mentioned
previously can apply.
·
The statistical operations for this
scale are counting, ranking, addition, subtraction, mean, standard deviation, Pearson
product-moment correlation etc.
For
example;
Concerning
observed quantities we can say that objects having assigned number of 5 and 10
are as far apart on the scale as two other objects having assigned number of 15
and 20.
Other
example;
Intelligence,
Temperature, learning score etc.
Ratio scale;
The measurement scale in which number
are assigned to the variable values in such a way that the level of measurement
is broken sown on a scale of equal units and the zero value on the scale us
absolutely zero is called ratio scale.
Properties;
·
It is strongest and best level of measurement.
·
It captures the properties of nominal,
ordinal and intervals scales.
·
It posses the attributes of magnitude, equal
intervals and an absolute zero point.
·
All the postulates mentioned previously
are applicable.
·
The statistical operations for this
scale counting, ranking, addition, subtraction, multiplication, division, and
all statistical applications.
For
example, Age, Height, weight, duration, number of items etc.
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