This article deals with meaning and definition of measurement and scales of measurement in education and statistics.

1. MEASUREMENT AND SCALES OF MEASUREMENT
1.1 MEASUREMENT
Measurement is a set of rules for assigning numbers to represent objects, traits, attributes or
behaviours.Measurement is to find a number that shows the amount of something. A measurement
unit is a standard quantity used to express a physical quantity. Measurement is a process of
determining how large or small a physical quantity is as compared to a basic reference quantity of the
same kind. In our daily lives, we use different forms of measurement at home, work and in other day
to day activities. While cooking a cup of coffee, we have to add water, milk coffee powder and sugar
in proper amount by measuring with the help of certain measuring instruments. For that we are using
different measuring instruments. We cannot exist without measurement, we have to measure physical
properties like length, weight, temperature, pressure, volume, time, size, distance, speed, energy etc.
for which humans have developed accurate measures. In the physical sciences measurement is the
activity of obtaining and comparing physical quantities of real-world object and events by using
scientific devices. In physical measurement, various measuring equipment are needed and
measurement is very accurate. A unit of measurement is a definite magnitude of a quantity, defined
and adopted by convention or by law, that is used as a standard for measurement of the same kind of
quantity. Any other quantity of that kind can be expressed as a multiple of the unit of
measurement. For example, a length is a physical quantity. The metre is a unit of length that
represents a definite predetermined length. When we say 10 meters, we actually mean 10 times the
definite predetermined length called "metre". Measurement is a process of determining how large or
small a physical quantity is as compared to a basic reference quantity of the same kind. Physical
measurement is the measurement of the object which has absolute existence, accurate and
quantitative, and there are some set of tools for physical measurement all over the world.
Measurement in behavioural sciences comprises the measurement of mental processes, traits, habits,
tendencies etc. mental measurement there is no surety of the accuracy measuring devices in terms of
quantitative measures in the form of marks or grades. Examine the example, Hans height is 160cm
and his score in Mathematics achievement test is 100. Here the data regarding the relevant
measurements of a child’s physical and mental measurements are given in precise quantitative terms.
Height is a physical quantity and hence it is measured with help of a scientific instrument and
measurement is given in meters and this measurement is very precise, accurate and scientific. While
his score in Mathematics is measured with the help of an achievement test prepared by the teacher for
her classroom assessment and hence it is subject.

2. Measurement refers to the process by which the attributes or dimensions of some physical object are
determined. When used in the context of learning, it would refer to applying a standard scale or
measuring device to an object, series of objects, events or conditions, according to practices accepted
by those who are skilled in the use of the device or scale.
Teaching, learning and assessment is an integrated process. A teacher normally attempts at measuring
child’s scholastic and co-scholastic aspects using various tools and techniques like tests, rating scale,
checklist, anecdotal records, observation, cumulative record etc. He usually represents the results of
these measurements in terms quantitative measures in the form of marks or grades. This process is
what we generally indicate by the term educational measurement. It is also known as mental
measurement or ‘psychological measurement’. It is always relative and there is no absolute zero. For
example, for measuring the intelligence of a person we have to take the help of intelligence tests
which are subjective in nature. Through his response, we can know the level of intelligence of the
person concerned. Mental measurement is both qualitative and quantitative in nature, and there are no
fixed tools for such measurement i.e., the same set of tools may not be applied to different types of
persons
1.2 Concept of Educational Measurement by different educationists
Measurement is the process of quantifying observations [or descriptions] about a quality or
attribute of a thing or person Thorndike and Hagen
Measurement is the assignment of numerals to objects or events according to certain rules.
James M. Bradfield
Measurement results are some score or numerical value and quantitative descriptions of the
pupils. J.P.Guilford
Measurement is a process of obtaining a numerical description of the degree to which an
individual possesses a particular characteristic . Norman E. Gronlund.
Measurement is a process by which we assign numbers to express the quantity of an object
or trait.
Measurement can be defined as a set of rules for assigning numbers to represent objects,
traits, attributes or behaviours.
Measurement is the process of assigning symbols to the dimension of phenomenon in order to
characterise in order to characterise the status of phenomenon as precisely as possible.
Measurement involves the process of quantification. Quantification indicates to what extent a
particular attribute is present in a particular object. It is the act or the process of ascertaining
the extent or quantity of something.
Measurement is the process by which a characteristic of an object, person or activity is
perceived and understood on specific standards and is described in standard words, symbols
or definite units.

3. By analysing the above definitions, it can be said that measurement is the process of quantification of
some phenomena, objects. It is to assign a number or a set of numbers to one or a setoff phenomenon.
In this process comparison is made of a quantity with an appropriate scale for the purpose of
determining the numerical value.
1.3 Characteristics of Measurement
• It is a process of:quantification of something.
• Assignment of numerical value or symbols
• Comparing an unknown quantity with a known, with an appropriate scale or unit.
• Determining magnitude of a variate.
• Answers the question “how much”
1.4 Process of measurement
Step-1: identifying and defining the quality or attribute that is to be measured
Some attributes or constructs can be measured directly. For example, height, weight,
blood pressure etc. can be measured directly using certain instruments. In behavioural
science, we usually must use more indirect ways to measure constructs, so we have to
develop a number of items to assess the construct. The construct is a proposed
attribute of a person that often cannot be measured directly, but can be assessed using
a number of indicators or manifest variables. In psychology, a construct is a skill,
attribute, or ability that is based on one or more established theories. Constructs exist
in the human brain and are not directly observable. So the first step in measurement is
to identifying and defining the quality, construct or attribute that is to be measured;
Step-2: Determining operations to isolate and display theattribute
The second step is to develop a procedure to find out and invent a set ofoperations
which will isolate the attribute of interest and display it. That is determining a set of
operations by which the attribute may be made manifest and perceivable. There areattributes
like length or weight for which we can use well standardized instruments and units of
measurement,but if we are measuring intelligence, or honesty or any dimension of
personality, we have to determine the set of operations; this is called operationalizing
the attribute or operational definition. For example, operational definition of creativity
refers to the score obtained by an individual on a standardised test developed based on
the Torrance theory of creativity.
Step-3: Quantifying the Attribute
The third step of the measurement process is establishing a set of procedures or definitions
for translating observations into quantitative statements of degree or amount. That isassigning
numerals to quantify the aspect of measurement or the attribute. This quantification helps
incommunicating about the attribute more efficiently and precisely. If quantificationhas been
done according to a set of rule (this is known as scale), we canapply mathematical operations
for making the measurement more meaningful.
For example, heights can be measured in centimetres or inches, interest can be measured
using rating scale.

4. 1.5 Scales of Measurement
A scale is a system or scheme for assigning values or scores to the characteristic being
measured (Sattler 1992). There are four scales of measurement, and these different scales
have distinct properties and convey unique types of information. The four scales of
measurement are nominal, ordinal, interval and ratio scale.
Nominal scale
Nominal scales are the simples of the four scales. It provides a qualitative system for
categorizing people or objects into categories, classes or sets. For example, gender is
an example of a nominal scale that assigns individuals to mutually exclusive
categories.This isascale of measurement in which the scale values represent categories
that only differ from one another qualitatively (i.e., differ in “type” rather than in
“amount”). In other words, the different values of a variable are categories that only
represent different “types” of something. Variables measured using a nominal scale
are also known as "qualitative" variables.
Ordinal scale
Ordinal scale measurement we can rank people or objects according to the amount or
quantity of a characteristic they display or possess. Hence ordinal scale enables us to
quantify the variables under examination. A scale of measurement in which the scale
values represent categories that differ quantitatively in terms of their order, but in
which the intervals between numbers (i.e., between categories) cannot be assumed to
be equal.Ordinal indicates “order”. Ordinal data is quantitative data which have
naturally occurring orders and the difference between is unknown. It can be named,
grouped and also ranked. For example, ranking the children in a classroom according
to their height from the tallest to shortest.
Interval scale
An interval scale is one where there is order and the difference between two values is
meaningful. A scale of measurement in which the distance between any two adjacent
scores is the same as the distance between any other two adjacent scores. However,
there is no “true” or “natural” zero point and therefore meaningful ratios cannot be
formed. In short, numbers are spread across equal intervals without a natural zero
point. which is measured along a scale, in which each point is placed at equal distance from

5. one another. Interval data always appears in the form of numbers or numerical values where
the distance between the two points is standardized and equal.Interval data cannot be
multiplied or divided, however, it can be added or subtracted. Interval data is
measured on an interval scale.
Ratio scale
Ratio scales have the properties of interval scale plus a true zero point that reflects the
complete absence of the characteristic being measured. With ratio scales, the scale
values are numbers that represent equal distances in some attribute, and there also is
an absolute zero point. This is a unique feature of ratio scale. Thus, meaningful ratios
can be formed. It is a type of variable measurement scale which is quantitative in
nature. It allows any researcher to compare the intervals or differences. For examples,
height measured in inches, which is a ratio scale, you may properly say that somebody
60 inches tall is twice as tall as somebody 30 inches tall.