Statistical variables come in four types- Nominal, Ordinal, Interval and Ratio. Qualitative or categorical data are usually measured using the nominal or ordinal scales. On the other hand we use the Interval and Ratio scales to measure quantitative data.
Nominal Data:
As the name suggests, nominal data refers to those data which have no intrinsic numerical value but are assigned numbers ‘in name only’. The numbers assigned to the data have no significance except as placeholders. This approach is generally used to organise categorical data. For example we may denote girls in a particular class as 0 and boys as 1 and get a string of the form,
10111100, which tells us that in this class there are 5 boys and 3 girls. Notice that nothing would have changed mathematically if we had denoted boys using 0 and girls using 1.
Some examples of nominal data are gender, eye colour, phone numbers, name and blood types. We can calculate the mode for a given set of nominal data but concepts such as median and mean do not make sense for nominal data. This is because we cannot assign an order to nominal data to calculate the median. Also it does not make sense to “add” nominal data to calculate the mean.
Ordinal Data:
As the name suggests, ordinal data refers to data that can be arranged in order and assign ranks. This is generally used to measure qualitative variables such as happiness, intelligence, singing ability, etc. We see many singing competitions where the participants are ranked in order of their ability. Now we can arrange the participants in order and find the median. The concept of mean still does not make sense for ordinal data.
The similarity between nominal and ordinal data is that in both cases we assign numerical values to quantities that are non-numerical in nature. The main difference between nominal and ordinal data is that nominal taken cannot be arranged in order whereas we can definitely assign order to ordinal data.
Interval Data:
Interval data is used to measure quantitative variables where there is no fixed standard of absolute zero. An example of interval data is temperature. We can assign numerical values to temperature but there is no standard zero value for temperature. For example, in temperature 0 Celsius is equal to 32 Fahrenheit. So a zero in one temperature scale may not be zero in another temperature scale. This is in opposition to quantities like length where an object of length zero remains so whether height is measured in meter or centimetre.
The main difference between ordinal and interval data is that in interval data successive differences between the data are equal while the same cannot be said for interval data. The difference between 36 and 37 degree Celsius is the same as the difference between 98 and 99 degree Celsius. On the other hand difference in singing ability between ranks 1 to 2 may not be the same as the difference in ability between ranks 9 and 10.
In addition to mode and median the concept of mean for interval data also makes sense. For example, we calculate things like the average temperature of a room, etc.
Ratio Data:
Ratio scale is used to measure quantitative data that has an absolute zero scale of reference. Some examples of Ratio data are speed, height, weight, etc. All these examples have a well-defined notion of zero. For example when we say zero speed we mean that the object is at rest.
So we see that the main difference between interval and ratio scales is that in the ratio scale we have well defined notion of absolute zero.
