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Actually, measurement is done on the indicants of the properties of objects. Indicant is merely a convenient word used to mean something that points to something else. For instance, if a boy continually strikes underlying hostility.

Or.

Measurement is the assignment of numerals to object or events according to some rule.

A numeral is a symbol used to distinguish objects from each other. The term assignment means that mapping of objects of one set into the objects of another set. A function f is the rule of mapping. For instance, the equation y=f(x) maps the elements of the set x to the elements of set y by the functional relationship f.

Example.

In a family , a3 a5 are males and a2, a4 are females, then the mapping of the set on the basis of the gender is Lets symbols 1 and 0 are represented male and female perspectives.

Thus, a measurement may be defined as the mapping of objects of one set of objects of another set. The kind of measurement achieved is a function of the rule which assigns the numerals 9symbol) to objects observations. The rule is called a scale.

- The first steps are to define the objects of the universe of discovering.
- The second step is to define the properties of the objects.
- Then the universe ‘U’ is partitioned into at least two mutually exclusive and exhaustive subset I,e each object is assigned to one subset and all object.

Example

Let U= all students of B.SC III year of a college. Suppose the characteristic to be measured is gender, then U is portioned into two mutually exclusive subsets. B and C where B is the subset of U which includes all males of U and C is the subset of U which included all females of U so that U=B+C.

**Postulates of measurement**There are basic postulates of measurement which concern about the relationship between the objects being measured . These postulates are.

$$1\,.Either\,X=Y\,or\,X≠Y\,But\,not\,both$$

$$2\,.If\,X=Y\,and\,Y=Z\,then\,X=Z$$

$$3\,.If\,X>Y\,and\,Y>Z\,then\,X>Z$$

Postulates 3 is true in the case of physical measurement but may not be true in a case of behaviour measurement.

For example.

Wife dominates husband and husband dominant child. It is not necessary that wife dominates child instead child may dominate mother.

- Nominal scale
- Ordinal scale
- Interval scale
- Ratio scale

**1. Nominal scale**

It is the lowest level of measurement. In this scale, numerals or the symbols are assigned to objects in order to distinguish one object from other. The numerals or symbols used have no numerical meaning. They cannot be added or ordered. The requirement of a nominal scale is simple. The first requirement is All the members of the set are assigned the same number or symbols and no two sets are assigned the same numerals or symbols. The second requirement is that postulates 1 and 2 are satisfied. Assignment of numeral symbols to football players are an example of nominal scale.Since the classification is the major objective of the nominal scale, it is also called classification scale. In nominal scale, the scaling operation is the partitioning of the given universe into a number of the mutual subset. The member of any one subset must be equivalent in the property being scaled.For example.Assignment of numerals to football players . Since the classification is the major objectives of the nominal scale . It is also called classification rule.**2. Ordinal scale**In this scale postulates, 3 is satisfied. The groups are compared to show one is high more than other. The characteristics of a scale are that all objects within a group are equivalent and each and every member of a group is greater than each and every member of another group. An example of the ordinal scale is the grading of services personnel’s such as colonel, Major Captain Spray, Hawaldar etc. In this scale, symbols used to denote the superior of one from the other.

Symbols used in ordinal scale denotes rank order and nothing more.

For instance, two subjects have the ranks 6 and 5 and other subjects the ranks 6 and 3, we cannot say that the difference of ranks in the 1

**3.Interval scale**It is an extended form of ordinal scale when the distance between any two numerals must be exactly known. To make it possible therefore an interval scale is characterised as the common and constant unit of measurement which assigns the real number to all pairs of elements in the ordinal scale. This makes the ratios of any two intervals independent of the unit of measurement and the zero point. That’s , it is irrelevant whether the unit of temperature is taken as 0F or 0C. Both the unit provides the same amount of information. This is because the units can be transferred to one another by certain relationship.

$$C/100=F-32/180$$

For example.

Water freezes at 0

**4. Ratio scale**It is an extension of an interval scale . The extension is made by including a true zero point at its origin. In this scale, the ratio points are independent of the units of measurement.

For example.Measurement of height, weight have true zero points and the height measured in ft or cm the weight measured in pounds or grammes have the identical ratios. The numerals associated with the ratio scale are true numbers with a true zero.

Reference

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