Level of measurement refers to the relationship between the numeric values of a variable and the characteristics that those numbers represent. There are five major levels of measurement: nominal, binary, ordinal, interval, and ratio. The five levels of measurement form a continuum, because as one moves from the nominal level to the ratio level, the numeric values of the variable take on an increasing number of useful mathematical properties.
Nominal variables are variables for which there is no relationship between the numeric values of the variable and characteristics those numbers represent. For example, one might have a variable "region," which takes on the numeric values 1, 2, 3, and 4, where 1 represents "North," 2 represents "South," 3 represents "East," and 4 represents "West." Region is a nominal variable because there is no mathematical relationship between the number 1 and the region North, or the number 2 and the region South, and so forth.
For nominal variables, researchers cannot compute statistics like the mean, variance, or median because they will have no intuitive meaning; the mode of the distribution can be computed, however. Nominal variables also cannot be used in associational analyses like covariance or correlation and cannot be used in regressions. To use nominal variables in associational analyses, the nominal variable must be separated into [Page 422]a series of binary variables. Only nonparametric statistical tests can be used with nominal variables.
Binary or "dummy" variables are a special type of nominal variable that can take on exactly two mutually exclusive values. For instance, one might have a variable that indicates whether or not someone is registered to vote, which would take on the value 1 if the person is registered and 0 if the person is not registered. The values are mutually exclusive because someone cannot be both registered and not registered, and there are no other possibilities. Like with nominal variables, there is no mathematical relationship between the number 1 and being registered to vote, but unlike nominal variables, binary variables can be used in associational analyses. Technically, only nonparametric statistical tests should be used with nominal variables, but the social science literature is filled with examples where researchers have used parametric tests.
Ordinal variables are variables for which the values of the variable can be rank ordered. For instance, a researcher might ask someone their opinion about how the president is doing his job, where 1 = strongly approve, 2 = somewhat approve, 3 = somewhat disapprove, and 4 = strongly disapprove. In this case, the values for job approval can be ranked, and researchers can make comparisons between values, for example, saying that someone who gives a job approval value of 1 approves of the president more than someone who gives a job approval value of 3.
However, a researcher cannot make exact mathematical comparisons between values of the variable; for example, it cannot be assumed that a respondent who gives a job approval of 4 disapproves of the president twice as much as someone else who gives a job approval of 2. Researchers can, however, compare values using "greater than" or "less than" terminology and logic.
The mode and the median can be computed for an ordinal variable. The mean of an ordinal variable is less meaningful, because there is no exact numerical "distance" between the number assigned to each value and the value itself.
Ordinal variables can be used in associational analyses, but the conclusions drawn are dependent upon the way that numbers were assigned to the values of the variable. For instance, reassigning the values of job approval such that "strong approval" is now a 5, "somewhat approval" becomes a 4, and so on, would change the sign of the correlation between job approval and another variable. Thus, the associational relationship observed between two variables is a by-product of both the way the ordinal variables were coded and the underlying relationships in the data. Technically, only nonparametric statistics should be used with ordinal variables, but the social science literature is filled with examples where researchers also have used parametric statistics.
With interval variables, distances between the values of the variable are equal and mathematically meaningful, but the assignment of the value zero is arbitrary. Unlike with ordinal variables, the differences between values assigned to the variable are meaningful, and researchers use the full range of parametric statistics to analyze such variables.
As with ordinal variables, interval variables can be used in associational analyses, but the conclusions drawn are dependent upon the way that numbers were assigned to the values of the variable. Interval variables can be rescaled to have a different value arbitrarily set to zero, and this would change both the sign and numerical outcome of any associational analyses. Parametric statistics can be used with interval variables.
With ratio variables, distances between values of the variable are mathematically meaningful, and zero is a nonarbitrarily assigned value. Anything that can be counted—votes, money, age, hours per day asleep—is a ratio variable.
Values assigned to ratio variables can be added, subtracted, multiplied, or divided. For instance, one can say that a respondent who views 6 hours of television per day views twice as many hours as another respondent who views only 3 hours, because for this variable, zero is nonarbitrary. By contrast, one cannot say that 60 degrees feels twice as warm as 30 degrees, because 0 degrees is an arbitrary construct of the temperature scale.
With ratio variables, researchers can calculate mean, median, mode, and variance and can use ratio [Page 423]variables in the full range of parametric associational analyses, with meaningful results.