## Introduction

Levels of measurement, also called scales of measurement, tell you how precisely variables are recorded. In scientific research, a variable is anything that can take on different values across your data set. Based on the kind of project you are collecting the data for, it is important to define the level of measurement for every variable that you plan to collect the data for.

## Objective

Get a high-level understanding of levels of measurement: By the end of this article, you should be able to identify the various levels of measurement that can be used in collecting data.

Variable is something that can take values from pre-defined data set. Based on what kind of values a dataset contains or a variable can be assigned to, there are 4 levels of measurement.

Nominal: Data is categorized. Like the list of 50 states in the US.

Ordinal: Data can be categorized and ranked. Survey answers set like never, sometimes, always.

Interval: Data can be categorized, ranked, and evenly spaced. Temperature scale

Ratio: Data can be categorized, ranked, evenly spaced, and has a natural zero. Height, Age, and weight

As you can see the classification is based on the complexity of the measurement, in increasing order with nominal being the least complex and Ratio being the most complex.

For each of these levels of measurement, let's look at what kind of mathematical operations, Central tendencies, and variabilities can be used

As you can see the more complex the data is the more complex operations that can be performed on data. Also, precision increases as the level of measurement increases.

One important thing to be noted is that some variables can fall into more than one level of measurement, based on the way you plan to use it. For example, You could record a person's age, either to fall in groups where it becomes ordinal. Or if you choose the person's exact age, it becomes a ratio. However, when collecting data, it is always recommended to collect the data at the highest precision level possible, as it allows for more precise analysis.

More Examples of the various levels of data:

Nominal: Literally any categorical data, where there is no comparison and is a closed set is nominal, but here are some examples.

City of birth

Gender

Ethnicity

Car brands

Marital status

Ordinal: these could sometimes be categorical and sometimes numerical.

Top 5 Olympic winners

Language ability (e.g., beginner, intermediate, fluent)

Likert-type questions (e.g., very dissatisfied to very satisfied)

How often do you skip dinner (never, sometimes, half the times, all the time)

Interval: There might be "zero" values in this data, but these are just arbitrary measurements and not a true zero, e.g. 0 degrees is different on the Celcius scale and on the Fahrenheit scale.

Test scores (e.g., IQ or exams)

Personality inventories

Temperature in Fahrenheit or Celsius

Ratio: The zero in this kind of measurement means an absolute zero

Number of people in a household

Years of work experience

number of kids enrolled in a competition

Number of vehicles owned in the last 10 years

Number of new admissions in the ICU per day

Conclusion: Now with the examples, we are able to differentiate between the various levels of measurement.

References: https://www.scribbr.com/statistics/levels-of-measurement/