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.
Postulates 3 is true in the case of physical measurement but may not be true in a case of behaviour measurement.
Wife dominates husband and husband dominant child. It is not necessary that wife dominates child instead child may dominate mother.
Physical Scales and its types
The intensities or the categories of factors are measured by using a physical scale or sociometric/ Psychometric scales. There are four types of physical scales.
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 1st and 2nd pairs are equal.
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.
Water freezes at 0oC or 32oF have the same meaning and can be converted to one another by the relation.In this scale, quantitative meaning may be associated with the objects position so the arithmetic operation can be successful applied. In this scale, there not only in equivalent (=) as in nominal scale and greater than (.>) solution as in ordinal scale but also the ratio of any two intervals are specified. Because of this property, the scale is extensively used in the studies of physical scales.
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.
Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.