2. Measurement of variables
Measurement of variables is an integral part of a survey research
The main objective of this session is to review the following concepts
in the context of survey research.
• Variables
• Measurement of variables
• Level of measurement
• Data generating process
• Constructs
• Brief review of scaling technique
3. Variables
• Measurable or observable characteristic of entities under study
• The characteristic of an entity can be either numeric or non-numeric
• The value of a variable can therefore be either numeric or non-numeric
• Variables types: Categorical and Quantitative according to whether it has
non-numeric or numeric response
Examples:
1. Weight
2. Bank balance
3. Sex
4. Marital status
5. Religious affiliation
6. Means of communication
4. Variables
The first two variables are
numeric, since each of them
describes quantity in
numbers. Numeric variables
are also referred to as
quantitative variables.
The last four variables are non-
numeric, since each of them
describes qualities in non-numeric.
Non-numeric variables are also
referred to as categorical
variables.
The first five variables are
single response variables,
since each of them has only
one response
The first five variables are
single response variables,
since the response of each
individual is only one.
5. Measurement
• “measurement is the assignment of numbers or any other
symbols to entities or events according to a pre-specified set
of rules” (Stevens,1942)
Example : In anthropometric survey, for instance, children’s
height, weight and mid-upper arm circumference (MUAC)
are measured by instruments, age is measured by asking
children’s completed age in months, and sex is measured by
direct observation.
• Categorical variable can be measured by assigning numbers
to responses of categorical variables according to pre-
defined rules or coding scheme. For example, a researcher
can assign 1 for girl and 2 for boy in the above example.
6. Measurement
• The process of assigning distinct numbers to
distinct categories or categorical variable is called
coding and it is a part of the measurement of
variables.
• Coding scheme will not change a categorical
variable into a quantitative variable
• Coding can be done in some convenient way; the
code numbers do no speak themselves
7. Levels of Measurement
• Stevens proposed four levels of measurement of
variables: nominal, ordinal, interval and ratio
Nominal Level: Used to measure categorical variables whose responses
have no specific order.
Example: Gender has two responses (male and female); have no
ordering
If we assign 1 for female and 2 for male (or in the other way),
mathematically, 2 > 1. Does it mean that male is greater than female?
Similarly, the difference 2 – 1 = 1 or the ratio 2/1 =2 is mathematically
true, but it does not mean that difference between male and female is 1
or male is twice as high as female.
8. Levels of Measurement
• Ordinal Level: Useful to that categorical variable whose responses has
specific order
Example
• Variable: relationship with spouse
• Responses: 1. bad, 2. fair and 3. good
• These responses have order and we measure them by assigning 1 for bad, 2
for fair and 3 for good
• The extent of goodness increases as we move from ‘bad’ to ‘good’
• The ordering of data 1 < 2 < 3 make sense with respect to relationship since
‘fair is better than bad’ and ‘good is better than fair’
• However, the difference and ratio among data do not make sense
• Mathematically (2 – 1) = (3 – 2) but it does not mean that the difference
between poor and fair is the same as the difference between fair and good or
being ‘good’ is 3 times better than being ‘bad’
9. Levels of Measurement
• Interval and Ratio Level: These measurement levels are useful to
those variables that generate real numbers as data. Some software –
example SPSS – does not make any distinction between the two
measurement levels
• However, there is a difference between the two
Example
• 1. Educational level completed: 1, 2, 3, 4…..
• 2. Temperature in degree Celsius: …, -3, -2, -1, 0, 1, 2, 3, 4, ……..
• 3. Age in completed years: 0, 1, 2, 3,
10. Levels of Measurement
• In all these variables, the difference between values have
meaningful interpretation (give examples)
• What about the ratios?
• Temperature in Biratnagar today is 36 degree Celsius and that
in Olangchung Gola is 18 degree Celsius. Is it meaningful that
‘Biratnagar is twice as hot as Olangchung Gola today’?
• Barun is 14 and his father is 42. ‘Barun’s father is thrice as old
as he is’ makes sense and is meaningful
• Meaningful difference but no meaningful ratio Interval
scale and Meaningful difference with meaningful ratio
Ratio scale
• There is absolute zero in ratio scale, but zero is relative in
interval scale (zero degree Celsius does not mean absence of
temperature, but zero income means no income)
11. Levels of Measurement
• The weakest level of measurement is the nominal and the
strongest is the ratio; and the hierarchy is nominal, ordinal,
interval and ratio.
• Level of measurement has direct implication on data analysis
because it primarily demands for classification of entities into
categories, ordering relation and performing arithmetic
operations
• Nominal data can only be classified; ordering and classification
is possible for ordinal data; but no arithmetic operations are
possible in these levels of measurement
All the four arithmetic operations can meaningfully be applied to
the ratio and interval scale data, except division is meaningless
to interval scale data.
12. Levels of measurement
Respondent Sex
Male = 1, Female = 2
Social Status
Low =1, Medium = 2, High = 3
Score on
I.Q. test
Age
R1 1 1 30 18
R2 2 2 60 36
R3 1 3 40 22
Consider the following example which displays the measurements of four
variables of three respondents.
What happens if we change the coding scheme of sex as follows?
Female = 0 and Male = 1
What happens if we change the coding scheme of social status as follows?
Low = 3, Medium = 1 and High = 2
IQ score of R2 is twice as high as that of R1. Does it mean R2 is twice as intelligent as R1?
Age of R2 is twice as high as that of R1. Does it mean R2 is twice as old as R1?
13. Data
• Data are measured or observed values of variables.
In the process of data generation, variables play
dominant role by linking a group of entities and data
as can be seen in next slide
15. Data
• Categorical variables (nominal and ordinal scales)
with the aid of coding schemes generate code
numbers as data, while quantitative variables
(interval and ratio scale) generate numeric data as
per actual numeric response.
• Naming of variables and Documentation of coding
schemes are crucial steps during the process of data
organization.
• Data analysis scheme also differs according to the
highest level of measurement associated with the
variable concerned
16. More on Qualitative and Quantitative variables
• Quantitative variables are further classified into two groups –
continuous and discrete. This distinction is essential while
analyzing the data.
• Continuous variables are usually obtained by measuring.
Example include age, waiting time for a service. Since continuous
variables are real numbers, we usually round them. For example,
age is rounded to the whole year, even though age can be
measured to great accuracy on a continuous scale. Similarly,
waiting time to get a service is rounded to the nearest whole
minute.
• Discrete variables are usually obtained by counting. There are a
finite or countable number of choices available with discrete
data. Some examples of discrete variables are number of
employees, number of car accidents, household size, number of
children etc.
17. Concept of Construct
There are some characteristics or concepts that cannot be measured
as simply as variables been measured, mainly due to the involvement
of complexity (in terms of their meanings and measurements) with
the characteristics. Some examples of such concepts are human
development, poverty, intelligence, self-esteem, motivation, job
satisfaction, anxiety, social capital, community needs, financial
performance, service quality, brand loyalty and so on.
Such complex abstract concepts in social research are called constructs.
Both variables and constructs are concepts; however, variables are
directly measurable or observable but constructs are not. A different
type of instrument is required for measuring constructs. One such
instrument is scaling.
18. Scaling Techniques
In recent years, scaling technique has emerged as a popular method for measuring
variables/constructs. It is used in a wide variety of situations. For example, to
measure
• individuals’ preferences over products, services, objects, or candidates
• individuals’ attitudes toward a particular product, service, object
• constructs
Broadly speaking, scaling techniques are categorized into the following two
headings.
• Comparative scaling techniques
• Non-comparative scaling techniques
19. Comparative Scaling Techniques
In this case items are directly compared with each other.
Some comparative scaling techniques are summarized
in the adjacent table. Some examples of comparative
scales are presented below.
Example 1 (Paired Comparison Scale): What do you prefer tea or coffee?
Example 2 (Rank-order Scaling): Please rank the following newspaper from 1 to 5,
putting 1 for your most favorite through to 5 for your least favorite.
_____Kantipur
_____Sagarmatha
_____Kathmandu Post
_____ Naya Patrika
_____ Nagarik
20. Non-comparative Scaling Techniques
In this case each item is scaled independently of the others. Some non-
comparative scaling techniques are summarized in the adjacent table.
Some examples of rating scales are presented below.
Example 1 (Continuous Rating Scale): On a scale of 0 to 10, how would you rate your
supervisor? (Very bad) 0--------------------------------------------------------10 (Excellent)
Extremely poor Very poor Satisfactory Very well Extremely well
1 2 3 4 5
Example 2 (Itemized Rating Scale): On a five-point scale, please rate the research
proposal submitted by Binod.
