Different types of Variables

Different types of Variables

What is the difference between nominal, ordinal and scale?

In SPSS, we can specify the level of measurement as scale (numeric data on an interval or ratio scale), ordinal, or nominal. Nominal and ordinal data can be either string alphanumeric) or numeric. But what is the difference?

Nominal or categorical, ordinal and interval

In terms of variables, they are described as categorical (or sometimes nominal), or ordinal, or interval.  Let’s see the definition and look why they are important.

Categorical or Nominal

A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories. Examples are given below-

a.     Gender is a categorical variable having two categories (male and female) and there is no intrinsic ordering to the categories. 

b.    Hair color is also a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) and again, there is no agreed way to order these from highest to lowest. 

c.     Examples of nominal variables include region, zip code, or religious affiliation

A purely categorical variable is one that simply allows you to assign categories but you cannot clearly order the variables. 

Ordinal

An ordinal variable is similar to a categorical variable.  The difference between the two is that there is a clear ordering of the variables.  Examples are given below:-

a.     Economic status, with three categories (low, medium and high). We can classify people into these three categories, also can order the categories as low, medium and high.

b.    Educational experience (with values such as elementary school graduate, high school graduate, some college and college graduate). These also can be ordered as elementary school, high school, some college, and college graduate. 

c.     Examples of ordinal variables also include attitude scores representing degree of satisfaction or confidence and preference rating scores.

Interval or scale

An interval variable is similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced.  Examples are given below:-

a.     Annual income is a variable that is measured in dollars, and we have three people who make $10,000, $15,000 and $20,000. The second person makes $5,000 more than the first person and $5,000 less than the third person, and the size of these intervals  is the same.  If there were two other people who make $90,000 and $95,000, the size of that interval between these two people is also the same ($5,000). 

b.   Examples of scale variables also include age in years.

Why does it matter whether a variable is categorical, ordinal or interval? 

Statistical computations and analyses assume that the variables have a specific levels of measurement.  For example, it would not make sense to compute an average hair color.  An average of a categorical variable does not make much sense because there is no intrinsic ordering of the levels of the categories.  Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result.  Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable.  In short, an average requires a variable to be interval.  Sometimes you have variables that are "in between" ordinal and interval, for example, a five-point Likert scale with values "strongly agree", "agree", "neutral", "disagree" and "strongly disagree".  If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable.  However, in order to be able to use statistics that assume the variable is interval, we will assume that the intervals are equally spaced.