While analyzing data, one out of the four scales of measurement – nominal ordinal, interval, or ratio – is used. Allocating a particular scale to any variable can be a tough task. It is a crucial task to first comprehend the mathematical properties and then allocates the relevant scale of measurement. Knowing the mathematical properties is significant because then you can identify the mathematical functions that are allowed. The nominal scale has the minimum mathematical properties involved, followed by Ordinal, Interval, and Ratio scales. The Ratio scale has the highest mathematical properties. Let us now discuss some examples for each kind of measurement scale.
‘Nominal scale’ is used for items that don’t require any sequence, for example, a grocery list. Suppose you have to buy vegetables, fruits, yogurt, biscuits, and cakes. It will not matter if any item is at the top or bottom. You simply number the items from one to five or five to one (whichever way you like). It means that the numbers are allocated to the items just for the sake of classification. The ascending or descending order doesn’t make any difference. So in nominal scale, only counting is involved and there is no distance between any two items (scales).
‘Ordinal scale’ is used when the magnitude of a case is to be measured against that of another. A car race will be a very good and understandable example for this scale. In a car race, multiple cars are racing for the number one spot. But they all end up finishing one after the other. It is noteworthy that though there is an order of reaching the finish line, there is no symmetry in the duration between two cars reaching the finish line. For example, the second car reaches the finish line one minute after the first car; the third car reaches the finish line 56 seconds after the second car; and so on. So, the numbers will tell us the various gaps (distance) between two cars (scales).
The best example of an ‘Internal scale’ is a survey. In a survey, there might be certain questions to which the participants might have to give their opinions on a scale of one to five where the parameters are,
- Strongly believe,
- Disbelieve, and
- Strongly Disbelieve.
In this case, the magnitude (distance) between two levels (scales) is the same. Like, if the magnitude between levels 1 and 2 is ten, then the magnitude between levels 4 and 5 will also be ten. So the answers assist the surveyor to understand the quantum of units by which any particular case is higher or lower than another.
‘Ratio scale’ involves the maximum mathematical properties. All the probable mathematical operations such as addition, subtraction, multiplication, and division are involved in this scale. In this scale, the number zero has its significance. For example, while measuring the height or weighing something, if the outcome is zero, it means that there is no height or no weight, respectively. To show the significance of zero in this scale, we can also cite the example of zero-degree temperature. Using a zero in this scale allows us to identify the extent to which one case is greater or smaller than another.
How does the dependence or independence of various scales of measurements have an impact on the ultimate result?