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# Levels of Measurement in Statistics

Published by at August 31st, 2021 , Revised On July 20, 2023

Two of the essential things for performing statistical analysis of data are variables and levels of measurement for these variables. By now, you might have a firm grip on what variables are and how they are divided into further groups.

So, guess it is time to get to the second important thing in statistical analysis: knowing how to measure different variables. Being able to understand what different levels of measurement are and when to use them is a skill. Let’s get better at this skill together.

### What are Levels of Measurement in Statistics?

Level of measurement in statistics is a classification that describes the values assigned to different variables and the relationship of these variables with each other. So, we can say that level of measurement is used to highlight the significant information within the values. Four levels of measurement were developed by a psychologist named Stanley Smith.

We will discuss each of these in the next heading.

### What are the Types of Measurement Scales?

The four measurement levels from the lowest level of information to the highest are:

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

## Nominal Scales

This level of measurement has the least amount of information given. In the nominal level of measurement, values in the variable are only used for the purpose of classifying data. It can be in the form of letters, words, and alpha-numeric symbols.

For instance, you want to classify a group of people into different subgroups based on gender. You will have three gender categories, Male, Female, and Other. Female gender could be denoted by the letter F, male by M, and Others by O. Now, this type of classification, which clearly is not giving much information, is called the nominal level of measurement.

## Ordinal Scales

The second level of measurement in order is the ordinal level of measurement. It shows some ordered relationships between different observations of variables. Ordinal scales are used to show non-mathematical information such as happiness, frequency, satisfaction, and so on.

In short, this level of classification maintains an intrinsic order along with descriptive qualities of the variables. The descriptive qualities can be similar to those of the nominal scale. However, the former does not provide data regarding order or ranking.

For instance, a student gets 99 marks on a math quiz. The second top scorer gets 95, and the third scores 89. In this case, you have two kinds of information; the gender of each student and their scores. The ordinal level of measurement thus indicates the ordering of the measurements.

## Interval Scales

This scale is another effective measuring level as it opens doors for accurate statistical analysis processes. It is defined as the numerical scale in which the order of the variables can be measured by minus-ing the variables. So, it is:

Difference between Variables = Order of the Variables

All the variables that have constant, familiar and computable differences are categorized with the help of this scale. It offers all the properties of the ordinal scale in addition to the difference between variables. The only disadvantage to going with this scale is that it has no true-zero value or pre-decided starting point.

For example, 70 Degrees Celsius is much colder than 50 Degrees Celsius, and the difference is the same as the difference between 50 and 30 Degree Celsius. Thus, the difference of 20 Degrees Celsius in both intervals has the same meaning and interpretation.

## Ratio Scales

The last level of measurement is the ratio scale, which provides the most amount of data regarding different variables in a study. The ratio scale produces the order of variables, the difference between variables, and the value of true zero.

### How is the Value of Zero Calculated?

It is calculated by making an assumption. It is usually assumed that the variables, in this case, have an option for zero. Now, with this additional option of true zero quality, the descriptive analysis technique and varied inferential can be applied to the variables. Another thing this scale does is it can establish the value of absolute zero. Examples of ratio scales can be height and weight.

Moreover, in market research, this level of measurement is utilized to find out annual sales, market sales, the number of customers and reviews, the price of a future product, and the list goes on.

Here is a chart to help you skim through all the levels of measurements quickly.

Offered Information Nominal Ordinal Interval Ratio
The sequence of variables is established Yes Yes Yes
Mode Yes Yes Yes Yes
Median Yes Yes Yes
Mean Yes Yes
Difference between variables can be evaluated Yes Yes
Addition and Subtraction of variables Yes Yes
Multiplication and Division of variables Yes
Absolute Zero Yes

### Why are Levels of Measurements Important?

Having enough knowledge about the levels of measurement can help one decide how to interpret data from different variables. When you know that a measure is one of the four scales, you know that the numerical values represent certain information and add the missing gaps in your research or assess your assumptions in the most accurate ways.

Apart from that, you might also not struggle with finding the appropriate statistical analysis method based on the values assigned. Can you think of anything else?

It is significant to know about these levels of measurements in statistics because they can determine the type of statistical analysis method required to test a hypothesis or get specific results.
What is the difference between nominal and ordinal scales?
There is a similarity, but ordinal scales are more detailed than nominal scales. The descriptive qualities of the ordinal scale can be similar to those of the nominal scale. However, the former does not provide data regarding order or ranking. The four measurement levels from the lowest level of information to the highest are:
1. Nominal Scales
2. Ordinal Scales
3. Interval Scales
4. Ratio Scales

It is significant to know about these levels of measurements in statistics because they can determine the type of statistical analysis method required to test a hypothesis or get certain results.

There is a similarity but ordinal scales are more detailed than nominal scales. The descriptive qualities of ordinal scale can be similar to those of the nominal scale, however, the former does not provide data regarding order or ranking.