In talking about variables, sometimes you hear variables being described as categorical
(or sometimes nominal), or ordinal, or interval. Below we will define these
terms and explain 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. For example,
a binary variable (such as yes/no question) is a categorical variable having two categories (yes or no) and there is no
intrinsic ordering to the categories. 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. A purely nominal variable is
one that simply allows you to assign categories but you cannot clearly order the
categories. If the variable has a clear ordering, then that variable would be an
ordinal variable, as described below.
Ordinal
An ordinal variable is similar to a categorical variable. The difference between
the two is that there is a clear ordering of the categories. For example, suppose you
have a variable, economic status, with three categories (low, medium and high). In
addition to being able to classify people into these three categories, you can order the
categories as low, medium and high. Now consider a variable like 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. Even though we can order these from lowest to highest, the
spacing between the values may not be the same across the levels of the variables.
Say we assign scores 1, 2, 3 and 4 to these four levels of educational experience and we
compare the difference in education between categories one and two with the difference in
educational experience between categories two and three, or the difference between
categories three and four. The difference between categories one and two (elementary and
high school) is probably much bigger than the difference between categories two and three
(high school and some college). In this example, we can order the people in level of
educational experience but the size of the difference between categories is inconsistent
(because the spacing between categories one and two is bigger than categories two and
three). If these categories were equally spaced, then the variable would be an
interval variable.
Interval (also called numerical)
An interval variable is similar to an ordinal variable, except that the intervals
between the values of the numerical variable are equally spaced. For example, suppose
you have a variable such as annual income 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).
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 nominal 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 numerical.
Sometimes you have variables that are “in between” ordinal and numerical, 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 numerical, we will assume that the intervals are
equally spaced.
Does it matter if my dependent variable is normally distributed?
When you are doing a t-test or ANOVA, the assumption is that the distribution of the
sample means are normally distributed. One way to guarantee this is for the
distribution of the individual observations from the sample to be normal. However,
even if the distribution of the individual observations is not normal, the distribution of
the sample means will be normally distributed if your sample size is about 30 or
larger. This is due to the “central limit theorem” that shows that even
when a population is non-normally distributed, the distribution of the “sample
means” will be normally distributed when the sample size is 30 or more, for example
see Central limit theorem demonstration .
If you are doing a regression analysis, then the assumption is that your residuals are
normally distributed. One way to make it very likely to have normal residuals is to
have a dependent variable that is normally distributed and predictors that are all
normally distributed; however, this is not necessary for your residuals to be normally
distributed. You can see the following resources for more information: