MEASUREMENT OF SCALES | ECONOMETRICS|L-17|

scales of measurement

Scales of measurement is how variables are defined and categorised. Psychologist Stanley Stevens developed the four common scales of measurement: nominal, ordinal, interval and ratio. Each scale of measurement has properties that determine how to properly analyse the data. The properties evaluated are identity, magnitude, equal intervals and a minimum value of zero.

Properties of Measurement

Identity: Identity refers to each value having a unique meaning.

Magnitude: Magnitude means that the values have an ordered relationship to one another, so there is a specific order to the variables.

Equal intervals: Equal intervals mean that data points along the scale are equal, so the difference between data points one and two will be the same as the difference between data points five and six.

A minimum value of zero: A minimum value of zero means the scale has a true zero point. Degrees, for example, can fall below zero and still have meaning. But if you weigh nothing, you don’t exist.

The four scales of measurement

By understanding the scale of the measurement of their data, data scientists can determine the kind of statistical test to perform.

1. Nominal scale of measurement

The nominal scale of measurement defines the identity property of data. This scale has certain characteristics, but doesn’t have any form of numerical meaning. The data can be placed into categories but can’t be multiplied, divided, added or subtracted from one another. It’s also not possible to measure the difference between data points.

Examples of nominal data include eye colour and country of birth. Nominal data can be broken down again into three categories:

Nominal with order: Some nominal data can be sub-categorised in order, such as “cold, warm, hot and very hot.”

Nominal without order: Nominal data can also be sub-categorised as nominal without order, such as male and female.

Dichotomous: Dichotomous data is defined by having only two categories or levels, such as “yes’ and ‘no’.

2. Ordinal scale of measurement

The ordinal scale defines data that is placed in a specific order. While each value is ranked, there’s no information that specifies what differentiates the categories from each other. These values can’t be added to or subtracted from.

An example of this kind of data would include satisfaction data points in a survey, where ‘one = happy, two = neutral, and three = unhappy.’ Where someone finished in a race also describes ordinal data. While first place, second place or third place shows what order the runners finished in, it doesn’t specify how far the first-place finisher was in front of the second-place finisher.

3. Interval scale of measurement

The interval scale contains properties of nominal and ordered data, but the difference between data points can be quantified. This type of data shows both the order of the variables and the exact differences between the variables. They can be added to or subtracted from each other, but not multiplied or divided. For example, 40 degrees is not 20 degrees multiplied by two.

This scale is also characterised by the fact that the number zero is an existing variable. In the ordinal scale, zero means that the data does not exist. In the interval scale, zero has meaning – for example, if you measure degrees, zero has a temperature.

Data points on the interval scale have the same difference between them. The difference on the scale between 10 and 20 degrees is the same between 20 and 30 degrees. This scale is used to quantify the difference between variables, whereas the other two scales are used to describe qualitative values only. 

4. Ratio scale of measurement

Ratio scales of measurement include properties from all four scales of measurement. The data is nominal and defined by an identity, can be classified in order, contains intervals and can be broken down into exact value. Weight, height and distance are all examples of ratio variables.