Scales of Measurement: Types, Characteristics and Properties

Scales of measurement are defined as ways of collecting and analyzing data. Variables or numbers are defined and classified using different scales of measurement. Each level of the measurement scale has unique properties that dictate different uses of statistical analysis. It depends on the objective of the study and the type of data (qualitative or quantitative) on which the selection of the appropriate scale depends.

• Stanley Stevens, a psychologist, created four of the most widely used measurement scales: nominal, ordinal, interval, and ratio. 
• Each scale of measurement has characteristics that influence how the data should be analyzed. 
• Identity, magnitude, equal interval, and minimum value of zero are the properties that are evaluated by these scales.

Read More: Uncertainty in Measurement

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Key Terms: Scales of measurement, Nominal Scale, Ordinal Scale, Interval Scale, and Ratio Scale.

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What are the Scales of Measurement?

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When data is collected for the study, the next step is to analyze it based on the tools we used for data collection. For example, if one wants to collect qualitative data, one can use specific labels (nominal scales) from which respondents will choose their option. For quantitative data, interval scales and ratio scales can be used which make it possible for the researcher to represent the data using numbers. 

• For instance, the example of data collection to find out which cars people like to drive. 
• Such data can be collected using scales with specific labels such as electric cars, diesel cars, hybrid cars, etc. 
• Therefore, a nominal scale of measurement will be used for this purpose. 
• Similarly, if a researcher wants to find the weight of people in a town, a ratio scale of measurement can be used. 
• There are four scales of measurement in statistics, which are mentioned below:

1. Nominal
2. Ordinal
3. Interval
4. Ratio

These scales of measurement are written in a fixed order that specifies that the ordinal scale also has properties of a nominal scale, the interval scale has both nominal and ordinal scale properties, and finally, the ratio scale contains properties of all the above three scales of measurement.

Scales of Measurement

Read More: Measurement of length

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Nominal Scale

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A nominal scale, also called a categorical variable scale, is defined as a scale used to label variables in a specific classification and does not include a quantitative value or rank. This scale is considered to be the simplest of the four variable measurement scales. 

• Computations performed on these variables would be futile because the choices have no numerical value.
• There are cases where this scale is used for classification purposes - the numbers associated with the variables of this scale are merely tags for classification or segmentation. 
• These figures have no quantitative value, thus any calculations based on them would be useless.

Characteristics of Nominal Scale

A nominal scale variable is categorized into two or more categories. 

• The answer should fall into any of the categories in the nominal scale measurement.
• It is qualitative. 
• The numbers are used here for the identification of the objects.
• The numbers don’t define the object characteristics. “Counting” is the only permissible aspect of numbers in the nominal scale.

Properties of the nominal scale of measurement

A few properties of the nominal scale of measurements are– 

• It can sort variables but does not put them in any order.
• It does not indicate any numerical value.
• It is useful for qualitative data.

Read More: Dimensional Analysis

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Ordinal Scale

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A variable measurement scale that is used to display the order of variables but not the differences between them is known as an ordinal scale. These scales are frequently used to represent abstract ideas like frequency, pleasure, happiness, pain intensity, etc. The implementation of this scale is quite easy to remember because 'ordinal' sounds similar to 'order', which is exactly what this scale is intended to do.

• Ordinal scales are still descriptive and have internal order, but they lack a scale origin, making it impossible to determine the distances between the variables. 
• Descriptive scales imply the same tagging properties as nominal scales, except that ordinal scales also have relative positions of variables. 
• The origin of this scale is absent so there is no fixed beginning or "true zero".

Characteristics of the Ordinal Scale

A few characteristics of the ordinal scale are– 

• The ordinal scale indicates the relative ranking of the variables.
• It helps in identifying and describing the magnitude of a variable.
• Along with the information given by the nominal scale, ordinal scales provide the rankings of those variables.
• The interval properties are unknown.
• The surveyors can quickly analyze the degree of agreement regarding the identified order of variables.

Properties of the ordinal measurement scale

A few properties of the ordinal scale are– 

• It shows the ranking or rating of the variables.
• It does not assign any numerical value to the data. Therefore, it is also used for qualitative data such as nominal measurement scales.
• It has variables that can be placed in order such as heaviest to the lightest, rank of players or students, etc.

Example:

• School students ranking – first, second, third, etc.
• Restaurants ratings
• Assessing the frequency of events
  • Very often
  • Often
  • Not often
  • Not at all
• Assessing the degree of agreement
  • Totally agree
  • Agree
  • Neutral
  • Disagree
  • Totally disagree

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Interval Scale

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An interval scale is known as a numerical scale where the difference between these variables and the order of the variables is known. Variables with familiar, continuous, and countable differences are classified using an interval scale. It is also simple to remember the primary role of this scale, 'interval' which represents the 'distance between two entities', which helps achieve the interval scale.

• These scales are effective as they open the door to statistical analysis of the data provided. 
• Mean, median, or mode are useful in calculating central tendency in this scale. 
• The only disadvantage of this scale is that there is no pre-decided starting point or true zero value.
• An interval scale has all the properties of an ordinal scale, except that it provides a calculation of the difference between variables. 
• The main characteristic of this scale is the equal difference between objects.

Characteristics of Interval Scale

A few characteristics of the interval scale are– 

• An interval scale is quantitative because it can measure the difference between values
• It allows the calculation of the mean and median of variables
• To learn the difference between variables, you can deduct the values between the variables
• Interval scale is the preferred scale in statistics as it helps in assigning any numerical values to arbitrary values like emotions, calendar types, etc.

Properties of the interval scale of measurement

A few properties of the interval scale are– 

• It has the properties of both the scales i.e., nominal and ordinal.
• It indicates a meaningful separation between variables.
• The difference between the variables can be represented in numerical terms.
• It consists of variables that can be added or subtracted from each other.
• It provides a meaning to 0 (Zero) which was not possible in the case of the above two scales. For instance, zero degrees of temperature.

Example:

• There are situations where trend scales are treated as interval scales.
• Other than the temperature scale, time is a very common example of an interval scale because the values are already established, stable, and measurable.
• Calendar year and time also fall under this category of measurement scale.
• Net promoter score, Likert scale, Bipolar matrix table, Semantic differential scale, etc. are the most commonly used interval scale examples.

Read More: Absolute and Relative Error

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Ratio Scale

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A ratio scale is characterized as a variable measurement scale that distinguishes between known variables using genuine zero-value data in addition to ranking the variables. It is computed by assuming that the variables have an alternative of zero, that the difference between the two variables is equal, and that there is a certain order between the alternatives.

• With the true null option, various inferential and descriptive analysis techniques can be applied to the variable. 
• The fact is that the ratio scale does everything that the nominal, ordinal, and interval scales can do, even establishing a value of absolute zero. 
• The most appropriate examples of ratio scales are weight and height. 
• In market research, the ratio scale is useful for calculating market share, number of customers, annual sales, next product cost, etc.

Characteristics of Ratio Scale

A few characteristics of the ratio scale are– 

• The ratio scale features absolute zero.
• It does not have negative numbers due to its zero-point feature.
• It provides unique opportunities for statistical analysis. 
• Variables can be systematically Addition, subtraction, multiplication, and division of Variables are possibly orderly. 
• Mean, median and mode can be calculated with the help of a ratio scale.
• Ratio scales have unique and useful properties. 
• One such feature is that it allows unit conversions like Kilogram – Calorie, Gram – Calorie, etc.

Properties of the ratio scale of measurement

A few properties of the ratio scale of measurement are– 

• It is useful for quantitative data.
• It indicates the absolute value of zero which means if the value is 0, it's nothing.
• Addition, subtraction, multiplication, or division is possible for the variables. 
• Additionally, computation of mean, median, and mode is also possible with this scale.
• it doesn't consist of negative numbers due to the feature of a true 0 value.

Example:

The below-mentioned questions come under the ratio scale category:

1. What is your daughter’s current height?

• Less than 5 ft.
• From 5 ft 1 inch to 5 ft 5 inches
• From 5 ft 6 inches to 6 ft
• More than 6 ft

2. What is your weight in kilograms?

• Less than 50 kilograms
• 51- 70 kilograms
• 71- 90 kilograms
• 91-110 kilograms
• More than 110 kilograms

Also Read:

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Things to Remember

• Scales of measurement are defined as ways of collecting and analyzing data. 
• There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.
• A nominal scale, also called a categorical variable scale, is defined as a scale used to label variables in a specific classification and does not include a quantitative value or rank. 
• A nominal scale variable is categorized into two or more categories. 
• An ordinal scale is described as a variable measurement scale that is used to show the order of variables, but it does not show differences between each variable. 
• An interval scale is known as a numerical scale where the difference between these variables and the order of the variables is known.
• A ratio scale is defined as a variable measurement scale that not only ranks the variables but also differentiates between known variables with true zero value information. 

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