Theories function tacitly as causal models for social phenomena. Frequently, theories are tested by statistical verifications of hypotheses derived from them (theories). The statistical procedures require that the data be quantified and reduced to numerical form. A wide variety of statistical techniques are available for analysis of data, depending in part, on the levels of measurement of the variables. The use of a particular statistical technique presupposes that the variables have been measured at certain levels. As we shall see later, the higher the level of measurement, the greater the variety of permissible mathematical operations that may be performed with the data, and the greater the level of sophistication of statistical techniques that can be used for data analysis.
A. Nominal Measures
The most basic measurement level is
the nominal measure in which the categories of a variable – the nominal
variable – differ only in name. the only relationship between the categories of
a nominal variable is that they are different from each other, and that no
category is necessarily higher or lower, greater or smaller, etc., than another
category. Knowledge of the criteria for placing individuals or objects into
categories which are exhaustive (include all categories) and mutually exclusive
(no case in more than one category), suffices for the attainment of this level
of measurement. Thus, the variable ‘sex’ with categories male and female which
are exhaustive (since these are the only two categories possible), and mutually
exclusive (since none can belong to both the categories at the same time), is a
nominal variable. This is because, the categories are just names only. We
cannot say that male is higher, better, and so forth, than female, or vice
versa. Similarly, the variable ‘religion’ with categories Islam, Christianity,
Hinduism, Buddhism, and other is a nominal variable.
It should be noted here that the researcher can arbitrarily assign numbers to the categories of a nominal variable, say, sex such as 1 for male and 2 for female. He will do equally well by assigning 5 for male and 2 for female. These numbers just label the categories, and no arithmetic operation can be performed on them. We cannot, for example, speak of average religion or average sex.
B. Ordinal Measures
A variable whose categories have an
ordered relationship is called an ordinal variable. In this measure, objects
can be ordered along a single continuum but the distance between the positions
are not meaningful. Thus, we can classify families according to social class
into the ordered categories: upper, upper middle, lower middle, and lower, or
classify individuals according to their religiosity into the ordered
categories: low religiosity, medium religiosity, and high religiosity. In
ordinal measures we have categories as well as order among the categories. In
this sense, ordinal measures are at a higher level than nominal measures that
have only categories. In ordinal measures we can not only categorize the
objects or individuals but also order them. As in nominal measures, the
researcher can also assign numerals to the categories of an ordinal variable.
For example, low religiosity, medium religiosity, and high religiosity may be
assigned numbers 1, 2, and 3 respectively. Here the numerals not only define
differences among the categories but also indicate ‘greater than’ or ‘less
than’ relationships. For example, an individual with 2 for the religiosity
variable may be thought to be more religious than an individual with 1 on the same
variable, and an individual with 3 may be thought to be more religious than an
individual with 2.
It should be noted that, as in nominal measures, arithmetic operations such as additions and subtractions also cannot be performed on numbers assigned to categories of ordinal variables. For example, for the religiosity variable we cannot add 1 and 2 and say that it is equal to 3. This will be equivalent to saying that low religiosity plus the medium religiosity equals high religiosity. But this is not the case, since we do not know the distance or interval between the categories. We do not know whether the distance between low religiosity and medium religiosity is the same as the distance between medium religiosity and high religiosity. It may so happen, for example, that individuals falling into the categories 1 and 2 do not differ much in terms of religiosity, while those falling into category 3 are very different from those falling into category 2. The ordinal measure tells us the greater than, more than, lower than etc. relationships, but not by how much greater, more, or lower.
C. Interval Measures
An interval variable is one in which the categories have an ordered relationship as well as the extract distances between categories are known. An interval variable has all the characteristics of both nominal and ordinal variables, and in addition, it has a constant unit of measurement. It provides equal intervals, however, from an arbitrary origin. An example of the interval measure is the measurement of temperature in centigrade scale. It is measured in terms of degrees, while no such measurement unit which remains constant from on situation to another exists to measure, for example, sex or religiosity. The difference between 60 and 61 degrees centigrade is the same as the difference between 30 and 31 degrees Centigrade. The distance between one category and the next is constant and is known. This means that the numbers representing categories in an interval measure can be added or subtracted in a meaningful way. But the ratio of two numbers is not meaningful. For example, we cannot say that 40 degrees is twice as hot as 20 degrees, neither can we say that a student who scored 90 in research methods test has twice the knowledge in research methods than a student who scored 45. This is because, both the temperature and the test score have arbitrary origins, since the zero degree, which is the freezing point of water, does not imply no temperature, and zero score in the test does not imply to complete lack of knowledge in research methods. There is some temperature at zero degree and at this temperature the water freezes. Similarly, a student who has scored zero in the test is unlikely to have had no knowledge of the attribute.
D. Ratio Measures
The ratio measurement is the highest
level of measurement. It has all the features of interval measure, and in
addition, an absolute or non-arbitrary zero implying that the zero value of a
ratio variable corresponds to the complete lack of the attribute. Thus zero
length implies no length at all, and zero children in a family implies that it
has no children. In this measure, multiplication and division are meaningful.
Thus, it is possible to state that a person 20 years old is twice as old as a
child 10 years old is twice as old as a child 10 years old. Some other examples
of ratio variables are height, time, distance and income.
An ordinal measure is a nominal
measure, and in addition, has the ordinarily property an interval measure is an
ordinal measure plus it has a unit of measurement; and the ratio measure has
all the properties of nominal, ordinal and interval measures plus it has an
absolute zero. This cumulative nature of these measures shows that a higher
level measure can be used as a lower level measure, but the converse is not
true. Thus, an interval variable, for example, can always be used as a nominal
or ordinal variable, but neither a nominal variable nor an ordinal variable can
be used as a nominal or an ordinal variable, but neither a nominal variable nor
an ordinal variable can be used as an interval.
Source: Methods and Techniques of Social Research by Abu Jafar Mohammad Sufian