# Explanation of the different variable types in statistics?

One thing that has always tripped me up when trying to learn new methods in statistics is understanding what type of features/variables can this method be applied to.

The variable types that especially trip me up are

• Discrete
• Continuous
• Categorical
• Nominal
• Ordinal

What are some examples and simple explanations of these and other commonly used variables types.

• You could get explanations and examples of the different variable types from any introductory statistics book. Also see this and this links for brief explanations and examples. – Ayalew A. Jun 23 '15 at 5:45
• I think there are only two type of variables in statistics (continuous and discrete, or some people may say three, continuous and discrete). Categorical, nominal and ordinal are all discrete, Categorical may include nominal and ordinal, while nominal has no order (or rank), ordinal has some order or (rank). The Quantative and Qualitative classification is really confusing (at least to me). I think Qualitative is also Quantative in statistics. – Deep North Jun 23 '15 at 7:13
• @DeepNorth I used to think quantitative meant that there was some continuous function with the data but it looks like this only applies to regressive data. – grasshopper Jun 23 '15 at 7:25
• Stevens' level of measurement typology is commonly used (and the division in this question is partly based on that one); in that typology discrete numeric variates are either ratio or interval, but in statistics they're generally treated differently from continuous ratio or interval variates. (That typology and the one in your question are also not the only way to divide up variable "types") – Glen_b Jun 23 '15 at 8:56
• This question is misguided, I am afraid. It is a mistake to use Stevens' typology to decide whether or not a statistical method can be applied to data. This can--and does--seem to rule out powerful, appropriate methods (such as Poisson regression for continuous responses). It misleads people into thinking that selecting a statistical procedure is merely a matter of figuring out a variable "type." It also has misled many into overlooking the rich, complex variety of data, ranging from counts to differences to proportions to sounds to images and more, that don't fit into this classification. – whuber Jun 23 '15 at 15:10

I was able to find a diagram from this page that clarified a lot of the original confusion.

• A continuous variable is a numeric variable. Observations can take any value between a certain set of real numbers (height, age, temperature, ect..)
• A discrete variable is a numeric variable that only consist of integers (number of kids, cars, pets,ect...)
• An ordinal variable is a categorical variable that can be ranked (grades,pizza size,levels of satisfaction)
• A nominal variable is a categorical variable that can't be ranked (race,religion, sex)
• That is very nice. That is what I often use to describe variable types. – Ayalew A. Jun 23 '15 at 8:53
• Stevens actually defined these variables differently, in terms of the groups of mathematical transformations that could be applied to them. Tukey, a short time later, thought it important to emphasize the fact that measurement type should not be considered a determiner of the form of statistical analysis. For instance, Tukey (and others) developed powerful techniques to analyze ordinal data as if they were continuous. Also note that this sense of "discrete" is much narrower than recognized by statistical theory: it seems to be describing count data. What happened to Stevens' ratio type? – whuber Jun 23 '15 at 15:14

You are mixing variable types with variable qualities Think of variables as a collection of qualities: {ordered, unordered} {discrete, continuous} {fininte, infinite} {known, unknown} (in terms of numeric value)

Categorical - {{discrete},{unordered},{finite}} Ordinal - {{discrete},{ordered},{finite,infinite},{known,unknown}} Numeric -{{discrete,continuous},{ordered},{known}}

• Nominal is synonymous for Categorical and Qualitative – mandata May 4 '16 at 3:44
• Numeric is synonymous for Quantitative, and is sometimes called Continuous – mandata May 4 '16 at 3:45
• Ordinals are indexed by integers; that is the number you care about. – mandata May 4 '16 at 3:59