Measurement & Scaling

Measurement

1.What do we mean by ‘Measurement’?

 Measurement is the fundamental aspect of any research.

 It is used in every sphere of our life.
 Measurement is the assignment of numbers to objects or
 events according to rules.
 Number is a symbol which can be provided in different ways like 1, 2, 3, ……
or I, II, III, ……. . Number should be explained to get the information. Symbols
have no quantitative meaning, it is simply a symbol of special kind. It can be
used to label objects, such as nurses, physicians or individuals drawn in a sample
from a universe/population.
 Symbols are the means of finding out the character of any events. A number
which when assigned for an event or character becomes quantitative meaning.
 A rule is a guide, a method, a command that tell us what to do.
 It is easy to measure physical products such as length, breath, height, weight, etc.
But measurement of qualitative facts is very difficult.
 Thus, it is essential to provide number or symbol to measure characteristics of
qualitative facts which is known as measurement.

Definitions:

According to Stevens, “Measurement is the assignment of numerals to objects or events

according to rules.”

According to Goode and Haff, “Measurement is the method of turning the series of
qualitative facts into a quantitative series.”

Thus, measurement is the act of providing numbers/symbols to the characteristics of the

events, products, perceptions, or thinking etc.

2. Why numbers are to be assigned?

 In a research, numbers are usually assigned for two reasons:

a) numbers permit statistical analysis of data, and
b) numbers facilitates the communication of measured rules and results.
 Example: If a researcher intends to find out the satisfaction level of nursing services of a
hospital then he/she can give ‘1’ to absolutely dissatisfied perception and ‘5’ to
absolutely satisfied perception. The researcher find out the satisfaction level of patients
by analyzing those numbers.

Importance of Measurement

3. Why measurement is important?

 Measurement is the fundamental basis of any physical and social science research.
Measurement is the act of providing numbers or symbols to the characteristics of
the events, products, perceptions, or thinking etc. So, it is very important in
research work. Some importance of measurement are as follows:
 Helps to identify variables
 Helps to measure
 Helps to Scientific test
 Helps to increase reliability of research.

I. Helps to identify variables

 Measurement provides numbers to the various characteristics of the product,

event or problems which helps to identify one character from another character.

II. Helps to measure

 Generally, subjective facts can not be measured. Measurement provides numbers

or symbols to them which helps to measure the subjective facts into numbers.

III. Helps to Scientific test

 Measurement provides numbers to the qualitative facts. Assignment of numbers

makes possible to the use of various mathematical and statistical tools for the test
of such qualitative facts scientifically.

IV. Helps to increase reliability of research

 Measurement provides numbers to the qualitative facts that makes possible to the
use of mathematical and statistical model. The result had drawn from the use of
mathematical and statistical tools remains always more reliable . Thus, it helps to
increase the reliability of research.
 Scales of measurement/ Scaling

 Measurement scale is defined as a plan that is used to assign numbers to

characteristics of an event.
 Scaling is an activity of creating continuous values for the objects as per the
importance of measured characteristics they posses.
 For example: Scale that is often used in research is the scale for sex.

Sex Scale

Male 1

Female 0

Types of Scale:

4. What are the different types of scales or scales of measurement?

 Different measurement scales are used on the basis of nature of data. Stevens has
classified the scales of measurement into four types, they are as follows:
 Nominal scale
 Ordinal scale
 Interval scale
 Ratio scale

I. Nominal scale

 A nominal scale is the lowest level of measurement. Nominal scales are just
names.
 In this scale, numbers or the symbols are assigned to objects in order to
distinguish one object from other.
 The number or symbols used have no numeric meaning. They cannot be added,
subtracted, multiplied, divided, or ordered (or ranked).
 In nominal scale, all the members of a set are assigned the same number or
symbol and two sets are not assigned the same number or symbol.
 Nominal scale classifies the events, product, individual or group providing
number or symbol.
For example:

Gender : Male (1) Female (2)

Religion : Hindu (1) Buddhist (2) Muslim(3)

Occupation : Business (1) Teaching (2)

Service (3) Agriculture (4)

(Remember that such codes do not make them quantitative)

 Nominal scales are exhaustive in nature, mutually exclusive, distinct, discrete and
non-continuous.

[ When nominal scale is used for classification purposes, the nominal scale serves as
labels for classes or categories. The classes are mutually exclusive and collectively
exhaustive. The objects in each class are viewed as equivalent with respect to
characteristic represented by the nominal number. All objects in the same class have the
same number and no two classes have the same number. ]

Permissible/Admissible Operations On Nominal Scale:

The only permissible operation on numbers in a nominal scale is counting i.e. Counting
of frequency.

Only a limited number of statistical operations based on frequency counts are

permissible, which are:

Percentage,

Mode,

Chi-square test,

Binomial test, etc.

Mathematical operations Such as addition, subtraction, multiplication and division are

not permissible. (Arithmetic calculations)
II. Ordinal scale

 This is the second level of measurement.

 An ordinal scale is a ranking scale in which numbers denote the order of the
objects or individuals.
 Numbers can be arranged from lowest to highest or from highest to lowest.
 Ordinal scale implies which object or individual is larger or smaller, more or less,
heavier or lighter, harder or softer than others. It indicates qualities that can
graded in definite order.
 An ordinal scale allows researchers to determine whether an object has more or
less importance than some other objects but not how much more or less.
 Therefore, an ordinal scale indicates relative position not the magnitude of the
difference between the objects. It shows the every event, product or variables in
ascending or descending order.
 [If any organization or researcher wants to determine the priorities then they use
ordinal scale like from beautiful to ugly, first to last etc. Such priorities can be
presented in numbers.]
 The numbers obtained from the measurement process indicate order rather than
exact quantity of the variables.

Example: Suppose a hospital wants to know the level of satisfaction of the patients with
nursing services of that hospital. This can be graded as: fully satisfied (1), partially
satisfied(2), not satisfied (3).

 It provides more information than nominal scale. It not only classifies the
variables but also categories the variables into different groups in a meaningful
category.
 The use of an ordinal scale implies a statement of greater than or less than without
stating how much greater or less.

Permissible/Admissible Operations On Ordinal Scale: Permissible statistics for ordinal

scales are:

 Median
 Mode
 Quartiles
 Deciles
 Percentiles
 Correlation coefficient based on ranking
 Non-parametric tests etc.
III. Interval Scale

 It is a combined form of nominal and ordinal scales.

 It needs equal distance on the scale represent equal values.
 It allows the researcher to compare the differences between objects.
 The difference between any two scale values is identical to another adjoined values.
 There should be constant or equal interval between scale values.
 This scale classifies the individuals, events, functions and variables into different
groups showing their difference.
 This scale has a starting and terminating point that is divided into equally spaced units
or intervals.
 An interval scale is characterized by a common and constant unit of measurement
which assigns a real number to all pairs of objects in the ordered set.
 In this measurement, the ratio of any two intervals is independent of the unit of
measurement and of the zero point.
 Interval scale is more powerful scale than nominal and ordinal scales.
 It is widely used in behavioral research. It is used to known the psychological features
and attitudes of human beings.
 Interval scale has no true zero point i.e. true origin.

Example-1: The age of Ram, Shyam, Hari and Krishna are older than Kalpana by 1,2,3, and
4 years. But we cannot claim Shyam is twice old than Ram because real age no one knows in
this case but we know only the interval.

Example-2: Suppose some scores for five students a, b, c, d and e are available.

o a b c d e
o 1 2 3 4 5

Intervals may be calculated as follows:

 Interval from a to c: c – a = 3 – 1 = 2
 Interval from c to d: d – c = 4 – 3 = 1
 Interval from d to e: e – d = 5 – 4 = 1
 Interval from b to d: d – b = 4 – 2 = 2
 Here we can say that score difference between students a and c and between b and d
would be equal.
Permissible/Admissible Operations On Interval Scale: Permissible statistics for interval
scales are:

 all the operations used in nominal and ordinal scales including the following:
 Arithmetic mean
 Standard deviation
 Range
 Product moment correlation
 Parametric tests etc.
 But some specified statistical calculations such as geometric mean, harmonic mean
and coefficient of variation are not meaningful on interval scale data.

IV. Ratio Scale

 Ratio scale is the most powerful and highest level of measurement.

 A ratio scale posses all the properties of nominal, ordinal and interval scales and in
addition, an absolute zero point.
 Thus, in ratio scale, we can identify objects, classify objects, rank objects and
compare intervals and differences.
 Numbers in the ratio scale indicate the actual amount of property being measured.

Example: Ratio scale is widely used in physical measure of weight, length, breath, time, are,
velocity, blood pressure, income etc.

 It is more used in physical research but very few in social science research. It is
specially used to find the relationship between two or more variables.
 [ The weight balance is good example of a ratio scale. It has an absolute zero which
allows us to calculate the ratio of difference between the weights of two individuals.]

Permissible/Admissible Operations On Ratio Scale: Permissible statistics for ratio scales

are:

 All mathematical operations

 All statistical operations.
 Parametric and non-parametric tests.