Nominal data and ordinal data are a sequence of gaining properties in data representation. In other words, ordinal data = nominal data + added property of “order”. Let us understand the difference and relationship between the two in depth:
- Scope and definition
Nominal data is simply labels without any relationship or order among them. For example, when someone asks us to list 4 animals, we can say “dogs”, “cats”, “elephants”, “horses”. In this list, each is independent of the other and has no order whether greater or smaller.
However, if someone asked us to list 5 animals in order of increasing sizes, then the same list would turn into “cats”, “dogs”, “horses”, “elephants”. This is now ordinal data because this is no longer just labels, there is a meaningful order.
- Relative position:
As we saw in the above example, nominal data doesn’t have a relative position. For example, when asked to list types of drinking glasses, we can say “wine glass”, “beer mug”, “stemless wine glass”, “whisky rocks”, “snifter” etc. Each has no relative position to the other and simply edits without any relationship to what is before or after.
Now for ordinal data, if someone asks to list glasses in the order of most preferred glass type to least preferred, then there would be an injunction of order into the listing. This would hence give rise to the relationship of what comes before and after.
- Categorical nature:
Both nominal and ordinal data have categorical labeling, with the difference that nominal data categories are exclusive of one another, while ordinal data categories have inherent relationship to one another.
For example, let’s say in a customer service survey a question is asked on the level of satisfaction on the quality of service. In this case ordinal data is used such as – “very satisfactory”, “somewhat satisfactory”, “somewhat unsatisfactory”, “very unsatisfactory”. As you can see, while each is a labeled category just like nominal data, there is an order and relationship between the categories.
- Lack of defined intervals:
Both nominal and ordinal data do not have any defined intervals between each label. From the example used above, there is no defined interval between “cats”, “dogs”, “horses”, “elephants” even when it is ordered based on sizes of animals. This is what differentiates nominal and ordinal data from interval data, which has the characteristics of nominal and ordinal + defined intervals.
- Mathematical representation:
Neither nominal data nor ordinal data allow for true mathematical representation due to a lack of defined intervals in both cases. However, numerical representation without true order is possible in both cases.
For example, if asked to list 5 random numbers, such as, 2, 67, 34, 65, 23, then this is nominal data.
However, when asked to list random numbers in increasing or decreasing order, then the list becomes ordinal data.
- Mathematical operations:
Mathematical operations in both nominal and ordinal data are limited to counting the occurrence of a specific type of value. For example, for ordinal data, in a customer service satisfaction survey, how many people selected “very satisfactory” from the list of options.
For nominal data mathematical operations the example can be – at a vet clinic, how many people bring in “dogs” vs how many bring in “cats”.
