Scales of Measurement

Data come in several different types. Here we review the four different kinds (NOIR): nominal, ordinal, interval and ratio.

describe data that do not have a specific numerical value

Nominal: these have no order to them, basically just categories. For example: color: “red”, “blue”, “yellow” — there are different kinds, but one isn’t necessary more than the other.
Ordinal: these do have an order, but the numerical difference between different values is not consistent or quantifiable. For instance, the finishers in a race. The difference in time to finish between the 1st place winner and 2nd place is not the same as the difference between 2nd place and 3rd place. While there is an order (or ranking), the winner may have taken 10 minutes, the second place 2 hours and third place 4 days.

describe data with a numerical value

Interval: the interval between two values is consistent across the range of values. For instance, the difference between 29F and 30F is the same as the difference between 43F and 44F. However, interval variables are different from ratio variables because zero is just another number on the scale, with no special significance – it is arbitrarily chosen.
Ratio: here the difference between two values has meaning, and the value of zero also has special meaning. Zero means there is none of the quality you are measuring. An example is time, the difference between 1 second and 2 seconds is the same as the difference between 123 and 124 seconds. And zero seconds means no time has elapsed. This zero value has inherent meaning.

With this scales of measurement problem set.