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Discrete and Continuous
Home What is Statistics? A Population and Sample A Parameter and a Statistic Quantitative and Categorical Data Discrete and Continuous Nominal, Ordinal, Interval and Ratio Describing the Center of Data Describing the Variability of Data The Standard Deviation and Coefficient of Variation The Empirical Rule Percentiles and The Five-Number SummaryView All Tutorials
 Describing the Center of Data
Fundamentals of Statistics 1: Basic Concepts :: Nominal, Ordinal, Interval and Ratio
You might have heard of the sequence of terms to describe data : Nominal, Ordinal, Interval and Ratio. They were used quite extensively but have begun to fall out of favor. These terms are used to describe types of data and by some to dictate the appropriate statistical test to use. Most statistical text books still use this hierarchy so students generally end up needing to know them.

Nominal basically refers to categorically discrete data such as name of your school, type of car you drive or name of a book. This one is easy to remember because nominal sounds like name (they have the same Latin root).    

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Ordinal refers to quantities that have a natural ordering. The ranking of favorite sports, the order of people's place in a line, the order of runners finishing a race or more often the choice on a rating scale from 1 to 5. With ordinal data you cannot state with certainty whether the intervals between each value are equal. For example, we often using rating scales (Likert questions). On a 10 point scale, the difference between a 9 and a 10 is not necessarily the same difference as the difference between a 6 and a 7. This is also an easy one to remember, ordinal sounds like order.  

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Interval data is like ordinal except we can say the intervals between each value are equally split. The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79 (although I know I prefer the latter). With attitudinal scales and the Likert questions you usually see on a survey, these are rarely interval, although many points on the scale likely are of equal intervals.  

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Ratio data is interval data with a natural zero point. For example, time is ratio since 0 time is meaningful. Degrees Kelvin has a 0 point (absolute 0) and the steps in both these scales have the same degree of magnitude.  

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Who Cares?
Where did this all come from you ask and why do we care?  Well, the short answer is, we should care most about identifying nominal data--which is categorical data. If it isn't nominal, then it's quantitative. So why all the fuss?  In the 1940's when behavioral science was in its infancy, there was much concern about trying to make the practice as legitimate as possible. Psychology and other Social and Behavioral Sciences are considered soft sciences as opposed to the hard sciences of Chemistry and Physics. It was thought that by applying some of the same thinking from the hard sciences, it would improve the legitimacy of these soft sciences--as well as the veracity of the claims made. 


One approach was to map types of scaling to more natural laws (something akin to the physical laws of gravity and motion). This classification system was proposed in 1946 by SS Stevens. In the article Stevens went so far as to say that you should only take averages on at least interval and ratio data. Nominal and Ordinal data should only be counted and described in frequency tables--no means and standard deviations. 

One of the more famous articles showing the fallacy of such rigid thinking was by an eminent statistician named Lord who in his article: "On the statistical Treatment of Football Numbers" showed how the means of nominal data can be meaningful too!

In practice, rating scales are ubiquitous in behavioral sciences and rarely have they been shown to have interval, much less ratio scales (what is the 0 point of customer satisfaction ?)

So means, standard deviations, t-tests, regressions and ANOVA are run daily and the results are published without much concern for these categories (to the chagrin of a few purists). What this classification system does remind us of is to not make interval and ratio claims about ordinal data. So if the average customer satisfaction on Product A is 4.0 and the Average on B is 2.0, we need to be careful in thinking the difference in satisfaction is twice. We can say there is a difference, but we're less sure if it's two times.

In summary, it's generally OK to take means and apply statistical tests to ordinal data, just be careful about making interval claims such as "twice as satisfied."

 
Discrete and Continuous
Home What is Statistics? A Population and Sample A Parameter and a Statistic Quantitative and Categorical Data Discrete and Continuous Nominal, Ordinal, Interval and Ratio Describing the Center of Data Describing the Variability of Data The Standard Deviation and Coefficient of Variation The Empirical Rule Percentiles and The Five-Number SummaryView All Tutorials
 Describing the Center of Data

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May 14, 2014 | anonomous wrote:
I didn't get an understanding of how nominal data could be used mathematically.
 
February 24, 2014 | Sherry wrote:
The concepts could have been expounded on further.
 
December 14, 2013 | wouter wrote:
why aren't there excersizes for me to practice? how am i supposed to know whether i understand it or not
 
December 8, 2013 | Danicka wrote:
ERRYTHANGGGGGGGGG
 
December 8, 2013 | Danicka wrote:
errythanggggg
 
November 4, 2013 | Beryl wrote:
Ratio data is not quite clear, how can time be zero? maybe more elaborate examples
 
October 22, 2013 | Shresthaparu wrote:
It is a really helpful site. It helped me to clear some of my confusions. Good work!
 
April 28, 2012 | anonomous wrote:
great site helped me put it all in perspective thanks
 
March 29, 2012 | olukoya aderonke wrote:
I ΔO̶̷̩̥̊͡η't understand †ђξ examples of ratiom pls I need about five examples of ratio datam
 
March 5, 2012 | Livinus Ikpa wrote:
Every detail made sense. However more examples should be given on the use of norminal and ordinal data in frequency tables. Good work!
 
June 27, 2011 | GLB wrote:
Great site. Thanks.
 
October 25, 2010 | vincent wrote:
what is 'natural zero point' ?
 
May 31, 2010 | onesmo mrope wrote:
it is good and easy to understand give us more
 
January 30, 2010 | Martha wrote:
I am still a little unclear about nominal and ordinal. Example: Movie ratings: G, PG, R. My book says this is nominal, but I'm stuck on the fact that they are rated or ranked according to language, violence, etc. and wonder why this wouldn't be ordinal? Same thing with sub-compact, compact, luxury cars. In my mind, this would be ordinal b/c they are "ranked" (and priced accordingly).