# Nominal, Ordinal, Interval, Ratio Scales

## Understanding levels of measurement in Statistics

It’s very important for researchers to have a good understanding about the variables that they are examining, because the type of variables that we have will determine how we analyse the data. A ‘variable’ is a factor or phenomenon that we are measuring. A key characteristic of a variable is that it can change depending on the context that it is measured in. Variables can be classified into several different types, and can include:

**Dependent:**a dependent variable, or outcome variable, is a measure of what it is we are interested in investigating. A dependent variable is so named because its values ‘depend’ on the effects of an independent variable.**Independent:**an independent variable is one that instigates a change in the value of the dependent variable. An independent variable needs to have at least two values, or levels, associated with it.**Interest:**a variable of interest refers to the variable that we are most interested in or curious about for our research question. We would focus on this variable in our studies because its role in our research question is not clear.**Quantitative:**a quantitative variable is a variable that varies based on amount or a number, such has age or number of pets owned.**Categorical:**a categorical variable is a variable that varies based on kind or a category, such as gender or education level.**Continuous:**a continuous variable is a variable that is not limited to a specific number of responses or values.**Discrete:**a discrete variable is a variable where answers fall into specific categories.

Each variable that we investigate is associated with what is referred to as a ‘level of measurement’. Knowing this level of measurement is important, because this is what will help us decide how we should analyse our collected data.

### What is a nominal scale?

A nominal scale is a level of measurement where all the responses collected are classified into categories based on similarities or differences. Nominal scales are primarily used for categorical variables, where all variables are named or labelled by kind, with no specific ordering of the variables and no numbers associated with each of the options. Due to the nature of nominal scales we cannot perform statistics on nominal variables, but we can look at the frequency of how often each category is chosen. Common examples of nominal variables include gender (male, female, non-binary) or education (primary, secondary, tertiary, post-graduate).

For our dessert example, say we conducted a survey and asked 100 people to state what their favourite type of dessert is with the aim of identifying which type of dessert is the most popular. Some of the responses provided include ‘chocolate ice-cream’, ‘apple pie’, ‘pecan pie’, ‘chocolate eclairs’, ‘vanilla ice-cream’ and ‘almond croissants’. Using this information, we would classify chocolate and vanilla ice-cream together as ‘ice-cream’, apple and pecan pie together as ‘pie’, and chocolate eclairs and almond croissants together as ‘pastries’. Now that we have categories for our responses, we can determine which type of dessert is most popular by seeing how many responses fall under our assigned categories.

### What is an ordinal scale

An ordinal scale is a level of measurement where, in addition to categorising all responses, the responses are ranked in a specific order as order is important to the answers provided and therefore the results. To facilitate this, all categories of responses are assigned numbers where the position of the numbers represent the rank order of the responses. However, it’s important to note for ordinal scales that while the order of the variables is shown, these are descriptive only and the difference between the variables cannot be determined. Common examples of ordinal variables include satisfaction (satisfied, neutral, unsatisfied) or grades (fail, pass, credit, distinction, high distinction).

To continue our dessert example, say that you have been asked to sample seven new desserts at a restaurant and rank them in order of your preference, with 1 being the least liked and 7 being the most liked. You rank the desserts in the following way:

6 – Donuts

5 – Cake

4 – Pie

3 – Cheesecake

2 – Brownies

1 – Ice-Cream

Based on this information, we can infer that out of the available options you liked the pastries on offer the most, and the ice-cream the least. However, while this information provides the order of your preference, it does not tell us the difference in preference between the seven desserts.

### What is an interval scale?

Interval: An interval scale of measurement is where all variables are labelled, ordered and there is a meaningful interval between each of the options included in the scale. For an interval scale, the order of the variables is known and, unlike nominal and ordinal scales, the difference between variables is also known. Because we know the difference between options, we can calculate measures of central tendency (mean, median, mode) and frequency on interval level data. Interval scales can contain a zero value and can have negative numbers associated with it, but this zero is arbitrary. Common examples of interval variables include temperature and time. To illustrate the example of temperature, on a thermometer we can tell that a temperature of 30 degrees is higher (i.e. hotter) than a temperature of 20 degrees, which is the same degree of difference as temperatures of 5 and 15. For temperature, the value of 0 is arbitrary because negative temperatures (i.e. below 0) are possible. Keeping with our dessert example, say that you are at a restaurant and there are seven desserts on offer. We know that you like brownies the most, and donuts the least. You are asked to rate, on a scale of 1 to 10, the other dessert options and you give this data:

9.0

8.5 – Pastries

8.0 – Ice-Cream

7.0

6.0 – Cheesecake

5.0 – Pie

4.0 – Cake

3.0

2.0

1.0 - Donuts

Based on this information, we can infer that you like ice-cream twice as much as you like cake, and that you prefer pastries only slightly more than ice-cream. However, while this information is more descriptive of your dessert preferences, there is no true zero associated with this scale.

### What is a ratio scale?

A ratio scale is the same as an interval scale, in that it produces the order of the variables and makes the difference between variables known. However, a ratio scale also features a ‘true zero’ point, which indicates that there is a total absence of what you are measuring. Ratio scales are determined assuming that the option to include 0 exists, and as such does not give negative values. As ratio variables are quantitative in nature, inferential and descriptive statistics may be applied to analyse them. Common examples of ratio variables include weight and height; it is not possible to have negative a negative weight or height, indicating that zero is the lower limit. To return to our dessert example – say that you are a baker, and you are measuring how high your desserts rise as they bake. You determine that:

14cm – Cheesecake

12cm

10cm – Pastries

8cm

6cm – Donuts

4cm – Pie

2cm – Brownies

0cm – Ice-Cream

Because of the zero-value attached to our scale, we can determine that ice-cream does not rise at all (it would melt if we baked it!), and that cakes rise four times as much during baking compared to a pie.

### Important Notes:

Based on our research question, it’s important that we determine our variables and the right level of measurement to go with it because this would impact how we analyse and therefore interpret our data. Bear in mind that nominal scales are the least precise measurement scales, whereas ratio is the most precise. If we use the wrong type of scale, this could negatively impact our results and affect our conclusions. While you as the researcher will know the correct scale, most statistical software packages will assume that the data you are entering is ratio in nature and classify it in this way – but make sure to change this before you perform any analyses.

### Helpful References:

- Australian Bureau of Statistics (2021). Statistical Language – What are Variables? https://www.abs.gov.au/websitedbs/D3310114.nsf/home/statistical+language+-+what+are+variables
- University of New South Wales (2021). Types of data & the scales of measurement. https://studyonline.unsw.edu.au/blog/types-of-data
- An introduction to principles of research (2021) What is research