# Measurement Scales

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## What is a Measurement Level?

The level of measurement reflects the relationship among the values that are assigned to a variableâ€™s attribute. Knowing the level of measurement of a variable allows you to interpret its different values and also helps you decide which methods of statistical analysis are appropriate for the assigned values.Â

Within this article, we will explore the four main types of measurement scales to gain an understanding of how and when they are used.

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## Four Levels of Measurement

There are four fundamental levels of measurement, and they are:Â

1. Nominal Scale: A nominal scale, also known as a naming scale, uses variables that are simply â€˜labelledâ€™ and have no specific order.
2. Ordinal Scale: On an ordinal scale, all the variables have a name and a specific order.Â
3. Interval Scale: Variables on an interval scale have a name, order, as well as a specific interval between each variable option.
4. Ratio Scale: Ratio scales have all the characteristics of an interval scale (has a name, order, and interval), and additionally can accommodate the value of â€˜zeroâ€™ as well.Â

### Nominal Scale

The variables on a nominal scale are simply used to label or categorize certain attributes that are being measured. The variables take qualitative values that represent each category, and there is no intrinsic order between different categories.Â

Although nominal variables are qualitative and are generally only used to create categories, they can also take quantitative values as long as these values do not have numeric properties. This means that arithmetic operations cannot be performed using these numeric values.Â

The following is an example of how a nominal scale could be used in surveys:Â

• Male
• Female
• Other

As you can see, the categories on this scale simply have names and there is no quantitative indication of how far apart these three categories are.Â

### Ordinal Scale

In the ordinal measurement scale, attributes have a name and can also be ordered by rank. However, it is important to note that there is no â€˜standard orderâ€™ within an ordinal scale are therefore the difference between two attributes on the scale is not equal.Â

Ordinal scales are used to measure qualitative traits. This scale establishes a relative rank between attributes but has no standardised interval scale unlike the ratio scale and the interval scale. Additionally, values on the ordinal scale can be used to find the median and mode among the responses.Â

An example of a commonly used ordinal scale is the Likert scale:

• How satisfied are you with the product you received?Â
• Very Satisfied
• Satisfied
• NeutralÂ
• Dissatisfied
• Very DissatisfiedÂ

As reflected in the question above, each answer option on the Likert scale has a name and an order, however, there is no standardised interval between each option.Â

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### Interval Scale

The values on an interval scale have a name, order, and a standardised interval between each option. This means that all the values on the scale are placed at equal distances from one another. The interval scale is therefore an extension of the ordinal scale which doesnâ€™t have a standard distance between each point on the scale. The values on an ordinal scale can be used to conduct arithmetic operations such as addition and subtraction.Â

It is important to note, although interval scales have attributes that are equidistant, the scale has no zero value, unlike the ratio scale.Â

The following is an example of how an interval scale could be used in surveys:Â

• Which age group are you a part of?
• <15
• 15-25
• 26-35
• 36-45
• 46+

As reflected in the scale above, the categories have a name and order, and also have a standard interval between each option on the scale.Â

### Ratio Scale

The ratio scale is an extension of the interval scale as the variables on the ratio scale have a name, order, interval, and also a zero value. Therefore, to qualify as a ratio scale, the variable must have a zero variable as well. This zero-point makes it possible to perform arithmetic calculations beyond just addition and subtraction, but multiplication and division as well.Â

It is important to first study an object to see if it satisfies all the properties of the interval variable and also has a zero value before measuring it on a ratio scale.Â

The following is an example of how a ratio scale could be used in surveys:Â

• Paula is 40 years old and her daughter is half her age. How old is Paulaâ€™s daughter?
• 15
• 20
• 25
• 12

The answer options for this question are different age values. Age, weight, and money are common ratio scale variables as they have a 0 value. This allows respondents to conduct mathematical operations on the values provided (Paulaâ€™s daughter is 40/2 years old = 20 years old).

## FAQs on Nominal and Ordinal Scales

The level of measurement of a variable provides information on the relationship among the values that are assigned to a variableâ€™s attribute.

Â There are four types of measurement scales, namely;

• Nominal Scale
• Ordinal Scale
• Interval Scale
• Ratio Scale

The ratio scale is an extension of the interval scale; its variables have a name, order, interval, as well as a zero-point (an interval scale does not have a zero point). The values on an interval scale can only be used for arithmetic operations such as addition and subtraction whereas a ratio scale can be used for additional operations such as division and multiplication.Â

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