Ordinal or Interval
Graham Tall research@grahamtall.com
For an introductory discussion of these terms, select types of number.
Consider the following range of categories
| Response to question | Response to statement | Type of Number | |
| 1 | Male or Female | Nominal | |
| 2 | No Yes | Disagree Agree | Nominal or Ordinal |
| 3 | No Maybe Yes | Disagree Uncertain Agree | Ordinal |
| 4 | NO No Maybe Yes YES | S.D. D. Uncertain A. S.A | Ordinal or Interval |
| 5 | NO! No no? yes? Yes YES! |
S.D.! D. d? a? A. S.A.! |
Ordinal or Interval |
| 6 | NO!_________________YES! | S.D!_________________S.A! | Interval |
In row 1 the categories are either/or. Somebody must, for all practical purposes, be either male or female. Nominal or categorical data is exclusive, there are no half-way positions (this is one of the problems in social research where someone who has parents from two ethnic groups and considers themselves to be, say, both African Carribean and Anglo-Saxon. Only in a very racist society can the ignorant concept 'a touch of the tar brush' be used to indicate that anyone who is not 'pure' white must automatically be defined as 'black').
In row 2, however, with responses like yes & no or agree & disagree the underlying continuum evident in later rows is constrained and the respondent has to categorise themselves as one or the other, the response would therefore still be deemed as nominal.
In row 3, the continuum is demonstrated by the presence of a middle category. However, the data can only be considered as ordinal because there is no attempt to define the terminology used.
In rows 4 and 5, more and more clarification is given. I commonly use exclamation marks in the extreme categorised to emphasise the strength of the response - to respond to those means one is very clear in one's views. To indicate the separation of the two middle categories in row 5, the clarification for d? is 'I tend to disagree'. To illustrate the continuous nature of the dimension respondents are told that they if they are uncertain they can 'circle adjacent categories'; this means total uncertainty can be given by someone who believes that represents their view. To the writer this means that in rows 4 and certainly in row 5, the data is more than simply ordinal, it now has the key characteristics that allow it to be defined as interval.
Between rows 5 and 6, researchers may insert more and more categories, each category being carefully defined. The intention is clear, the intervals between each category become more and more identical, and the data is interval in nature.
In row 6, the continuous single line emphasises the interval position.
In scientific research, the above theoretical position needs to be justified by more than a philosophical argument. The analysis needs to be tested. It is common practice to accept attitude data as interval when the responses to a number of attitude questions are combined. But, the underlying belief that attitude data can be considered as interval in nature, is evident in factor analysis and cluster analyses. The reality is that such analyses, which rest on parametric tests, provide meaningful results. Literally 'the proof of the pudding is in the eating'.
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