1. LEVELS OF
MEASUREMENT
DR. RUPASI TIWARI
PR. SCIENTIST AND INCHARGE ATIC
ICAR-INDIAN VETERINARY RESEARCH INSTITUTE
IZATNAGAR, UP-243122, INDIA
2. Measurement is the assignment of numerals to objects or
events according to certain rules.
Measurement is the process of mapping aspects of a
domain onto other aspect of range according to some rules.(
C R Kothari )
WHAT IS MEASUREMENT ???
Domain
Whole set
of
students in
this class
Range
Male
or
female
3. Hence the mapping process is done by various scales
of measurement
i.e levels of measurement
9. exhaustive – comprehensive i.e include all possible
answerable responses
mutually exclusive - no respondent should be able to have two
attributes simultaneously (e.g., employed vs. unemployed - it
is possible to be both if looking for a second job while
employed)
QUALITIES OF VARIABLES
10. WHAT IS LEVEL OF MEASUREMENT?
the process of assigning values to the
attributes for a variable and drawing a
relationship among them .
11. WHAT IS LEVEL OF MEASUREMENT?
The process of assigning values to the
attributes for a variable and drawing a
relationship among them .
1 2 3
relationship
values
12. WHAT IS LEVEL OF MEASUREMENT?
The process of assigning values to the
attributes for a variable and drawing a
relationship among them .
1 2 3
relationship
values
attributes NCP Independent BJP
13. WHAT IS LEVEL OF MEASUREMENT?
The process of assigning values to the attributes for
a variable and drawing a relationship among them .
1 2 3
values
attributes
variable
NCP Independent BJP
Party Affiliation
14. helps you decide what statistical analysis
is appropriate on the values that were
assigned
helps you decide how to interpet the data
from that variable
WHY IS LEVEL OF MEASUREMENT
IMPORTANT?
15. the values just “name” the attribute uniquely
- categorizing
NOMINAL MEASUREMENT
16. the values just “name” the attribute uniquely
- categorizing .
does not imply any ordering of the cases
NOMINAL MEASUREMENT
17. the values just “name” the attribute uniquely
- categorizing .
does not imply any ordering of the cases
for example, jersey numbers in football
NOMINAL MEASUREMENT
18. the values just “name” the attribute uniquely -
categorizing .
does not imply any ordering of the cases
for example, jersey numbers in football
even though player 32 has higher number than
player 19, you can’t say from the data that he’s
greater than or more than the other
NOMINAL MEASUREMENT
20. when attributes can be rank-ordered
distances between attributes do not
have any meaning
ORDINAL MEASUREMENT
21. when attributes can be rank-ordered
distances between attributes do not have
any meaning
ORDINAL MEASUREMENT
22. when attributes can be rank-ordered
distances between attributes do not have
any meaning
for example if we say
A’s rank is 1 and B-2, C-3, D-4 , E-5
we can’t say that A is 4 times more
brilliant than D…..
ORDINAL MEASUREMENT
24. when distance between attributes has
meaning
for example, temperature (in Fahrenheit)
- distance from 30-40 is same as
distance from 70-80
INTERVAL MEASUREMENT
25. when distance between attributes has
meaning
for example, temperature (in Fahrenheit) -
distance from 30-40 is same as distance from
70-80
but note that ratios don’t make any sense - 80
degrees is not twice as hot as 40 degrees
(although the attribute values are)
INTERVAL MEASUREMENT
26. Almost no variables used in social science are interval-level
variables, with the exception of time measured in calendar
years. The interval between the categories 1902 and 1903 is
one year, the same as the interval between 1766 and 1767 or
between 2002 and 2003. So this variable has equal
intervals. But what about a zero point? When did time
start? Can we imagine an absence of time?
Philosophers or astronomers may have answers for these
questions, but in practical terms, there is no zero point.
Hence, time in years would be an interval-level variable.
But for practical purposes, we will ignore interval-level
variables and concentrate on nominal-, ordinal-, and ratio-
level measures.
27. has an absolute zero that is meaningful
RATIO MEASUREMENT
28. has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)
RATIO MEASUREMENT
29. has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)
for example,number of clients in past six months
RATIO MEASUREMENT
30. has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)
for example,number of clients in past six months
it is meaningful to say that “...we had twice as many clients in
this period as we did in the previous six months
RATIO MEASUREMENT
31. Name Harita Vijay Pranshu Priyanka Muthu
Gender Female male male Female male nominal
Rank 1st 2nd 3rd 4th 5th ordinal
DOB 1990 1991 1992 1989 1988 interval
Marks 100 98 95 93 90 ratio
EXAMPLE
33. THE HIERARCHY OF LEVELS
Nominal Attributes are only named; weakest
34. THE HIERARCHY OF LEVELS
Nominal Attributes are only named; weakest
Ordinal
35. THE HIERARCHY OF LEVELS
Nominal Attributes are only named; weakest
Attributes can be ordered
Ordinal
36. THE HIERARCHY OF LEVELS
Nominal
Interval
Attributes are only named; weakest
Attributes can be ordered
Ordinal
37. THE HIERARCHY OF LEVELS
Nominal
Interval
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Ordinal
38. THE HIERARCHY OF LEVELS
Nominal
Interval
Ratio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Ordinal
39. THE HIERARCHY OF LEVELS
Nominal
Interval
Ratio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Absolute zero
Ordinal
40. Nominal data are just counted data .
Mostly used in surveys and other ex-post –facto research
when data collected require only classification into major
subgroups
MODE is the measure of central tendency
Common test of statistical significance :– Chi-sqare test
POINTS TO REMEMBER….
41. Ordinal scale places events in order
is frequently used in research relating to qualitative
phenomena
Appropriate measure of central tendency is MEDIAN
CONTD…
42. Interval scale is
more powerful measurement than ordinal scale as it
incorporates the concept of equality of interval .only
addition and subtraction can be done to the variables.
Permissible statistical operation is MEAN
. tests for statistical significance are “ t ’’ test and “ F ’’
test
CONTD…
43. Ratio scale
has a absolute or “ true zero ” .facilitates a comparision
Ratio scale is the actual measure of variabls . Multiplication
and division can also be carried out with ratio scale .
Measure of central tendency is arithmetic and geometric
MEAN.
CONTD…
44. Interval and ratio data are parametric, and are used with
parametric tools in which distributions are predictable (and
often Normal).
Nominal and ordinal data are non-parametric, and do not
assume any particular distribution. They are used with non-
parametric tools such as the Histogram.
PARAMETRIC VS. NON-PARAMETRIC
