Difference between Categorical, Ordinal and Interval Variables

note Please refer to https://stats.idre.ucla.edu/other/mult-pkg/whatstat/what-is-the-difference-between-categorical-ordinal-and-interval-variables/

Different Types of Variables

Categorical

A categorical variable (or nominal variable sometimes) is one that has two or more categories, but there is no intrinsic ordering to the categories.

For example,

• gender: male, female
• hair color: blonde, brown, brunette, red ...

Ordinal

An ordinal variable is similar to a categorical variable.

The difference between these two is taht there is a clear ordering of the variables.

For example,

• economic status: low, medium and high
• educational experience: elementary school graduate, high school graduate, college graduate ...

note For educational experience example, the spacing between the values is not necessarily the same. For instance, the difference between elementary school and high school might be much bigger than that of high school and college.

Interval

An interval variable is similar to an ordinal variable, except that the intervals between the interval variable are equally spaced.

For example,

• annual income (measured in $): $10,000, $15,000, $20,000 ...

Why Variable Type Matters

tl;dr: an average requires a variable to be interval.

• An average of a categorical variable does not make sense (no intrinsic ordering), for example, average of hair color.
• An average of educational experience does not make much sense either, since the spaceing is very uneven.

note In order to be able to use statistics that assume the variable is interval, we will assume that the intervals are equally spaced.

Does it Matter if My Dependent Variable is Normally Distributed

When 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 sample size is about 30 or larger.

You should review Central Limit Theorem!