Classifying Variables by Type

Types of Variables

Nominal Measurement

Nominal measurements give names to values of a variable. For example, color is a nominal measurement with red, blue, and black as potential values. Of course we can code these names as numbers and make 1 signify red, 2 signify blue, and 3 signify black but the numbers would only identify the underlying color and would have no meaning as a number. Variables that use a nominal measurement scale have no underlying order among the values and should not be used in certain statistical procedures. For example, would taking the mean on a nominal variable have any meaning?

Ordinal Measurement Ordinal variables have some form of ordering that corresponds to the set of values the variable can have. For example, an opinion poll that uses a Likert scale of 1 to 5 (1- strongly disagree -- 3 agree -- 5 strongly agree) are ordinal variables. Unlike nominal variables there is an ordering and the numbers you select should maintain that ordering; however, the actual numbers you use to represent that ordering are not important.

Interval Measurements

Interval variables take on numeric values and the ordering of these values is important as are the differences between variables. Temperature is a good example of an interval scale.

Ratio measurements

Ratio variables take on numeric values and the ordering of these values is important as in the differences between variables. The difference with ratio variables is that the number zero (0) takes on special meaning. Speed is an example of a ratio measurement because a speed of 0 has special meaning. In the example on interval measurement, a temperature of 0 is not special, it is just another value in the set of potential values.

Discrete Variables

Discrete variables have a limited number of potential values in the set of possibilities. For example, the number of times I eat in a week can have a wide range; however it is certainly bounded by some upper cieling. Discrete variables also show up possessing the property that they occur in units. In the example above, I either ear or I don't, I can have an entry that states I eat 20.3 times that week, because what does .3 mean?

Continuous variables Continuous variables have an infinite number of potential values. The values can be bounded within a certain range but the potential list of values is still infinite. Many argue that there are few variables that can actually be considered continuous variables because our ability to measure values is so imprecise that the potential values are now finite. For example, taking someone's temperature, clearly the body can take on an infinite number of values; however using a thermometer to measure those values may restrict what we can use to a potentially small set rounded to the nearest tenth of a degree.

The key distinction to examine is whether a potential value could occur. For example, in the discrete example we know that we can't eat 20.3 times in a week, whereas in our temperature examine it is possible that our average temperature over a period is 98.7 degrees.

Why worry about this

The type of basic analysis you conduct is dependent on the measurement type of the variable. Nominal data really can only be analyzed with frequency tables and graphs. Ordinal data can also be analyzed with frequency tables and graphs as well as descriptive statistics. Interval and ratio data can use all the techniques of ordinal data as well as exploratory data analysis techniques.

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Author - Jack Suess
UMBC University Computing Services
Created - 1/15/96