Levels of Measurement: Nominal, Ordinal, Interval, and Ratio (with Examples)

In the field of statistics, variables and numbers are evaluated and classified using various measurement scales. The data level of measurement, also known as the scale of measurement, refers to the nature and characteristics of the data that are being collected or analyzed. 

The selection of a particular scale of measurement is based on the specific properties of the variables in question, and it determines the statistical analyses that can be applied to them. There are four commonly used levels of measurement:[1]  

• Nominal: The data can only be categorized into distinct categories without any inherent order.  
• Ordinal: The data can be categorized and ranked, but the distance between them cannot be measured.  
• Interval: The data can be categorized, ranked, and evenly spaced so that variables can be ordered, and the distance between them can be measured.  
• Ratio: The data can be categorized, ranked, evenly spaced, and has a natural zero.  

The level of measurement of a variable can significantly limit the analysis of data. Continuous level of measurement is supported by ratio and interval scales. These scales allow for infinitely fine subdivisions between points, enabling the representation of continuous data. Ratio scales, in addition to having equal intervals, also have a true zero point, which is crucial for supporting continuous measurement. This means that on a ratio scale, it is meaningful to say that one value is twice or half of another value, which is essential for many types of continuous measurements like weight, height, time, and temperature. Interval scales, while not having a true zero point, still support continuous measurement by providing equal intervals between points, allowing for precise and consistent comparisons.

Nominal, ordinal, interval, and ratio data 

Nominal, ordinal, interval, and ratio data are important because they provide a structured framework for understanding and analyzing different types of information. Nominal data consists of categories without any intrinsic order, such as gender or eye color. Ordinal data, on the other hand, has a clear order or ranking but the intervals between categories are not necessarily equal, like education level or Likert scale responses. Interval data maintains a specific order, and the intervals between consecutive points are equal and measurable, as seen in temperature measurements in Celsius or Fahrenheit. Ratio data, while also maintaining order and equal intervals, has a true zero point, indicating the absence of the attribute being measured, as observed in measurements like height or weight. Ratio and interval data allow for more advanced statistical techniques compared to nominal and ordinal data. 

What are levels of measurement in the statistics? 

The levels of measurement are vital indicators that determine the degree of precision with which variables can be recorded. The most rudimentary level of measurement permits only the exclusive categorization of a variable, whereas more complex levels allow for ranking, the inference of equal intervals, and the presence of true zero points. It is crucial to understand that the use of scales of measurement is imperative for accurate data collection and analysis across various fields, from test scores to temperature. Thus, the knowledge of these levels of measurement is of utmost importance for any researcher or data analyst. There are four main levels of measurement: nominal, ordinal, interval, and ratio. Each level of measurement has its own characteristics and determines the types of statistical analysis that can be applied to the data. 

1. Nominal Level: This is the simplest level of measurement, where data is categorized into mutually exclusive groups with no intrinsic order or ranking. Examples of nominal scales include gender (male, female) or eye color (blue, brown, green). Nominal data can only be classified and counted, and the only measure of central tendency that can be used is the mode. 
2. Ordinal Level: Ordinal scales categorize variables with a specific order or ranking, but the intervals between the categories are not necessarily equal or measurable. Examples of ordinal scales include educational levels (high school, college, graduate school) or customer satisfaction ratings (very dissatisfied, dissatisfied, neutral, satisfied, very satisfied). Ordinal data can be ranked and compared using the median and mode, but not the mean. 
3. Interval Level: Interval scales categorize variables with a specific order or ranking, and the intervals between consecutive points are equal and measurable. Examples of interval data include temperature measured in Celsius or Fahrenheit. Interval data can be added and subtracted, and measures of central tendency such as the mean, median, and mode can be used. However, multiplication and division are not possible for this level of measurement because there is no true zero point. 
4. Ratio Level: Ratio scales are the highest level of measurement and categorize variables with a specific order or ranking, and the intervals between consecutive points are equal and measurable, with a true zero point indicating the absence of the attribute being measured. Examples of ratio data include height, weight, and age. Ratio data can be added, subtracted, multiplied, and divided, and all measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation) can be used. 

Why are levels of measurement important? 

Levels of measurement are crucial because they inform analysts about the nature of the data and the types of analyses that can be performed.[2] For example, ordinal data allows for comparisons based on a specific hierarchy, while interval data enables analysis of the exact distances between items. For example, using a t-test on ordinal data would not be appropriate, as the t-test assumes interval or ratio data. Thus, understanding these levels of measurement helps in planning research, as it dictates the resources needed to collect data with specific properties, such as a true zero point in ratio data. Moreover, the levels of measurement guide how research findings are presented; interval data might be visualized in charts, while ratio data could involve mathematical equations. 

Characteristics of nominal, ordinal, interval, and ratio scales 

The characteristics refer to the properties or attributes that describe how data is organized, represented, and manipulated in a computer system or programming language. Understanding the characteristics of levels of measurement is essential for efficient data management and processing. Here are the common characteristics of each data type:[3] 

1. Nominal Scale: 
   • Categories are mutually exclusive, meaning each observation belongs to only one category. 
   • Categories are exhaustive, meaning all possible categories are included. 
   • No mathematical operations can be performed on nominal data (e.g., you cannot find an average or perform arithmetic operations). 
2. Ordinal Scale: 
   • Categories have a meaningful order or ranking (e.g., low, medium, high). 
   • Intervals between categories are not uniform or measurable. 
   • Arithmetic operations (like addition and multiplication) are not meaningful, but some non-arithmetic operations (like median or mode) can be performed. 
3. Interval Scale: 
   • Has all the properties of ordinal scales. 
   • Intervals between points are equal and consistent. 
   • Zero point is arbitrary and does not indicate the absence of the attribute being measured. 
   • Arithmetic operations like addition and subtraction are meaningful, but multiplication and division are not (e.g., you can say 10°C is 20°C warmer than 30°C, but you cannot say it is twice as hot). 
4. Ratio Scale: 
   • Has all the properties of interval scales. 
   • Has a true zero point, meaning that a value of 0 represents the absence of the attribute being measured. 
   • All arithmetic operations (addition, subtraction, multiplication, division) are meaningful (e.g., you can say an object that weighs 20kg is twice as heavy as an object that weighs 10kg). 

This table summarizes the key characteristics of nominal, ordinal, interval, and ratio scales. 

Understanding these characteristics is crucial for choosing the appropriate scale for data collection and analysis, as well as for interpreting the results accurately to understand their differences and applications. 

Examples of nominal, ordinal, interval, and ratio scales 

1. Nominal Scale: This scale categorizes data into mutually exclusive groups with no intrinsic order. Examples include 
   1. Types of cars (e.g., sedan, SUV, truck) 
   2. Marital status (e.g., single, married, divorced) 
2. Ordinal Scale: This scale orders data based on a specific criterion but does not indicate the magnitude of the difference between each value. Examples include 
   1. Educational level (e.g., high school diploma, bachelor’s degree, master’s degree) 
   2. Likert scale responses (e.g., strongly disagree, disagree, neutral, agree, strongly agree) 
   3. Evaluating the frequency of occurrences (e.g., very often, often, not often, not at all) 
   4. Assessing the degree of agreement (e.g., totally agree, agree, neutral, disagree, totally disagree) 
   5. Net Promoter Score (NPS): NPS is often derived from survey responses where individuals are asked to rate, on a scale of 0 to 10, how likely they are to recommend a product, service, or brand to others. 
3. Interval Scale: This scale orders data based on a specific criterion, and the difference between two values is meaningful. However, it does not have a true zero point. Examples include 
   1. Temperature in Celsius or Fahrenheit (e.g., 0°C, 10°C, 20°C) 
   2. Dates (e.g., January 1st, February 1st, March 1st) 
   3. IQ scores (e.g., 80, 100, 120) 
4. Ratio Scale: This scale is similar to the interval scale but has a true zero point, where zero indicates the absence of the attribute being measured. Examples include 
   1. Height in centimeters or inches (e.g., 150cm, 170cm, 190cm) 
   2. Weight in kilograms or pounds (e.g., 50kg, 70kg, 90kg) 
   3. Time taken to complete a task in seconds, minutes, hours (e.g., 0 seconds, 30 seconds, 60 seconds) 
   4. Understanding these levels of measurement is important in understanding the nature of the data and determining appropriate statistical analyses. 

How do I know which descriptive statistics to use? 

Choosing the right descriptive statistics depends on the nature of your data and the specific aspects you want to describe. Here are some common descriptive statistics to use based on the level of measurement and data type. 

• Interval and Ratio Data: For interval and ratio data, which are quantitative and have a meaningful zero point, you can use the following. 

• Ordinal Data: For ordinal data, which have a natural order but the intervals between values may not be equal, you can use the following. 

•  Nominal Data: For nominal data, which are categorical and have no inherent order, you can use the following. 

These tables can be used as a guide to select the appropriate descriptive statistics based on the characteristics of your data. 

Key takeaways 

The present discussion has delved into the nuances of levels of measurement and how they impact the choice of descriptive statistics and analyses. Dividing data into nominal, ordinal, interval, and ratio categories is essential for several reasons.[2] Firstly, it helps in understanding the nature of the data and determining the appropriate statistical analyses that can be applied. Each type of data requires different statistical methods for analysis and interpretation. Secondly, it allows for clear communication and interpretation of data. By categorizing data into these types, researchers and analysts can effectively communicate the characteristics of the data and its implications. Additionally, it provides a framework for data organization and management, making it easier to store, retrieve, and analyze data. Finally, understanding these categories helps in making informed decisions in various fields such as research, business, and policy-making, as it provides insights into the relationships and trends within the data. 

Frequently asked questions 

1. What are the levels of measurement in a research study? 

The level of measurement of a variable impacts the precision and depth of analysis possible in a research study. Higher levels of measurement allow for more detailed insights into the data, while lower levels provide more general information. For example, consider gathering data on people’s income for a study on spending habits. There are different ways to measure income, each with varying levels of precision: 

• • Exact Figure: Participants provide an exact income figure. This allows for precise calculation of income variations across the dataset. 
  • Income Ranges: Participants select their income from predefined ranges (e.g., 10-19k, 20-29k, 30-39k). While this provides some information about income distribution, it lacks the precision of exact figures. 
  • Categorical Classification: Participants categorize their income as “high,” “medium,” or “low.” This is the least precise level of measurement as it does not provide numerical values or allow for detailed analysis of income variations.

2. What are the 4 levels of measurement? 

The four levels of measurement, in order from least to most precise, are 

• • Nominal: This is the simplest level of measurement, where data is categorized into distinct groups or classes without any specific order. Examples include gender, race, and eye color. 
  • Ordinal: In this level of measurement, data can be categorized and ranked, but the differences between the categories are not uniform or meaningful. Examples include survey responses like “strongly disagree,” “disagree,” “neutral,” “agree,” and “strongly agree.” 
  • Interval: Data at this level of measurement can be categorized, ranked, and the differences between the values are meaningful and consistent. However, there is no true zero point. Examples include temperature in Celsius or Fahrenheit. 
  • Ratio: This is the most precise level of measurement, where data can be categorized, ranked, the differences between values are meaningful and consistent, and there is a true zero point. Examples include age, weight, height, and time. 

Each level of measurement has its own set of properties and determines which statistical analyses are appropriate for the data. 

3. Is age a ratio or interval? 

When it comes to levels of measurement, age is typically considered a ratio variable. Ratio variables have a true zero point, meaning that a value of zero indicates the absence of the variable being measured. In the case of age, a person’s age of 0 would indicate that they have not yet been born. Additionally, ratios between values are meaningful; for example, a person who is 30 years old is twice as old as a person who is 15 years old. 

4. Why are levels of measurement important? 

Understanding the level of measurement of data is crucial for selecting appropriate statistical methods, interpreting results accurately, and drawing valid conclusions in research and data analysis. Using the wrong level of measurement can lead to incorrect interpretations and conclusions. 

5. Which levels of measurement are qualitative? 

Qualitative data levels are descriptive and categorical and are typically associated with nominal and ordinal levels of measurement.  

• Nominal: Qualitative data at the nominal level consist of categories with no inherent order or ranking. Examples include gender, race, and marital status. 
• Ordinal: Qualitative data at the ordinal level also represent categories, but they have a clear order or ranking. For example, educational level and economic status. 

 6. Is gender ordinal or nominal? 

Considering levels of measurement, gender is typically considered a nominal variable, as it represents categories or labels (e.g., male, female, non-binary) rather than a scale with a specific order. However, in some contexts, gender can be treated as an ordinal variable if there is a specific order or hierarchy implied (e.g., in some cultures where gender roles are strictly defined). For instance, in some discussions about gender roles or gender identity, there may be a progression or hierarchy (e.g., “male,” “female,” “non-binary”), which could be seen as ordinal. 

References: 

1. Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in health sciences education, 15, 625-632. 
2. MacKay, D. M. (1969). Information, Mechanism and Meaning. Cambridge Mass. 
3. Williams, M. N. (2021). Levels of measurement and statistical analyses. Meta-Psychology, 5. 

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