Level of measurement - the basic of any social science research methodology

1. Sanchita Garai, Sanjit Maiti & K S Kadian
Dairy Extension Division
ICAR-National Dairy Research Institute
Karnal-132001, Haryana
www.ndri.res.in
Sanchita.bckv@gmail.com
Basic Postulates and Level of Measurement in Social Research

2. Postulates of Basic Measurement
 A postulate is a statement assumed to be true without need
of proof of any kind.
 A postulates states an assumption that we make about some
relationship between objects.
 The nine postulates are essentially those proposed by
Campbell and repeated after him with variations (9. 15, 18,
and 26).
 The first 3 postulates have to do with identities. The next two
postulates have to do with the establishment of order. The
last four have to do with additivity.

3. 1. Either a=b or a≠b
2. If a=b, then b=a
3. If a=b, and b=c then a=c
4. If a>b, then b<a
5. If a>b and b>c then a>c
6. If a=p and b>0 then a+b>p
7. a+b=b+a
8. If a=p and b=q then, a+b = p+q
9. (a+b)+c =a+(b+c)
Nine postulates are

4. The first postulate establishes identity of a number. Numbers
are identical or they are different
1. Either a=b or a≠b
2. If a=b, then b=a
The second postulate states that the relation of equality is
symmetrical.

5. The above postulate expresses in equation form the
familiar dictum: “things equal to same thing are equal
to one another”.
This postulate points out that the relation > is
asymmetrical.
3. If a=b, and b=c then a=c
4. If a>b, then b<a

6. The fifth(above) postulate is a transitive statement
5. If a>b and b>c then a>c
 The sixth postulate indicates the possibility of
summation.
 It is also implies the fact that the addition of zero
leaves a number invariant.
6. If a=p and b>0 then a+b>p

7. The seventh postulate means that the order in which things are
added makes no difference in result
7. a+b=b+a
8. If a=p and b=q then, a+b = p+q
The eighth postulate means that identical objects may substitute
for one another in addition.
Finally, the ninth postulate means that the order of combinations or
associations makes no difference in addition.
9. (a+b)+c =a+(b+c)

9. Measurement is the assignment of a number to a
characteristic of an object or event according to
rules.
 Stevens proposed his typology in a
1946 Science article titled "On the theory of scales
of measurement
 In that article, Stevens claimed that all measurement in
science was conducted using four different types of scales
that he called "nominal", "ordinal", "interval", and
"ratio", unifying both "qualitative" (which are described
by his "nominal" type) and "quantitative" (to a different
degree, all the rest of his scales)

10. Why is Level of Measurement Important
First, knowing the level of measurement helps you
decide how to interpret the data from that variable.
When you know that a measure is nominal (like the
one just described), then you know that the numerical
values are just short codes for the longer names.
Second, knowing the level of measurement helps
you decide what statistical analysis is appropriate on
the values that were assigned. If a measure is
nominal, then you know that you would never
average the data values or do a t-test on the data

12. Comparison of Different Level of Measurement
Incremental
progress
Measure property Mathematical
operators
Advanced
operations
Central
tendency
Nominal Classification,
membership
=, ≠ Grouping Mode
Ordinal Comparison,
level
>, < Sorting Median
Interval Difference,
affinity
+, − Yardstick Mean,
Deviation
Ratio Magnitude,
amount
×, / Ratio Geometric
mean,
Coefficient of
variation