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Levels of Measurement

Introduction

Depending on what you want to research or learn, several sorts of information are collected when gathering data. When undertaking any data gathering or analysis, it is important to know your data type. You’ll have a variety of variables in your dataset, and these variables can be recorded with varying degrees of accuracy. 

The four levels of measurement—nominal, ordinal, ratio, and interval—and their definitions will all be covered in this article, along with an exploration of each level through examples.

What are Levels of Measurement?

The level of measurement is a classification used in statistics that links the values given to variables with one another. In other words, the information contained in the values is described using the level of measurement.

Nominal, ordinal, interval and ratio are the four different levels of measurement. 

The Four Levels of Measurement

To provide interesting answers to questions, statisticians use data. The level of measurement is a classification used in statistics that links the values given to variables with one another. However, not all data is created equally. The type of various sorts of information is done using the four levels of measurement: nominal, ordinal, interval, and ratio.

( 1 ) Nominal 

The least amount of information is included in nominal scales. A nominal scale is the most basic measurement system we may use to name variables. Variables without quantitative values are labeled using a nominal scale. A nominal scale is a naming scale where variables are merely “named” or labeled with no particular order.

In some circumstances, a nominal scale is used to classify data; the numbers assigned to its variables serve just as labels for a category. These figures have no quantitative importance, so any calculations based on them are pointless.

Examples of Nominal Scales

The following are some examples of variables that can be measured on a nominal scale:

GenderMale, Female
Blood TypeA- , A+, B-, B+, AB-, AB+, O-, O+
Hair ColorBlack, Blonde, Brown, Grey, etc.
Eye ColorAmber, Black, Blue, Gray, Brown, Green 
Marital StatusSingle, Married, Widowed, Divorced, Separated

Characteristics of Nominal Scales

The characteristics of variables that can be measured on a nominal scale are as follows:

( a ) A variable is classified into two or more categories on a nominal scale. It is a level of measurement where the response to a given question can fall into either category. Categories are exclusive of one another. Let us say, for instance, that an individual cannot have both A- and O+ blood types. 

( b ) There is no natural order in nominal scales. For instance, it is impossible to rank variables like eye color, marital status, and blood type from least to greatest or best to worst.

( c ) Numbers on a nominal scale are assigned to specific objects because they do not specify the attributes of the corresponding objects. In a nominal scale, “counting” is the sole acceptable action in relation to numbers. For instance, we can count the number of single, married, widowed, etc.

( d ) We can only compute the mode as a measure of central tendency for these variables. Which category had the most counts is provided by the mode. For instance, we can find which blood type occurred most frequently in the data set.

( 2 ) Ordinal

Variables with a natural order but no quantitative difference in values are labeled using the ordinal scale. Ordinal scales are a higher degree of measurement since they provide more information than nominal scales.

Examples of Ordinal Scales

The following are some instances of variables that can be measured using an ordinal scale:

Degree of PainMinimal, Moderate, Severe, Unbearable Pain
Education LevelElementary, High School, College Graduate
Customer Level SatisfactionNot Satisfied, Slightly Satisfied, Satisfied, Very Satisfied, Extremely Satisfied 
Economic StatusLow, Medium, High
Military RankingsLieutenant, Captain, Major, Colonel, General 

Characteristics of Ordinal Scales

The ordinal scales have the following characteristics.

( a ) Natural order appears in ordinal scales. Let us take the classification of pain by the intensity in the following order: excruciating, severe, moderate, and minimum.

( b ) It is unknown what the interval’s characteristics are. It is impossible to quantify the value difference. Let us say, for example, that we cannot say that the difference between the degree of pain, minimal and moderate, is the exact difference between severe and excruciating.

( c ) Ordinal scales allow for median and mode computation. The median is the middle of the data set, while the mode is the category that occurred most frequently. 

( 3 ) Interval

Variables with the natural order, measurable differences between values, but no true zero value are characterized by interval scale. Because they guarantee no significant differences between values, interval scales provide more information than ordinal scales. In other words, interval scales are ordinal scales with equivalent scale values across the range of intervals from low to high.

Examples of Interval Scales

Some examples of interval scales are personal inventories, test scores, family income, the temperature measured in Celsius or Fahrenheit, etc.

Characteristics of Interval Scales

The interval scales have the following characteristics:

( a ) Given that the nominal and ordinal scales are qualitative, the interval scale is preferred. The interval scale is quantitative in that it allows for the quantification of value differences. The Interval scale is a preferred measurement scale in statistics or scientific analysis since it can facilitate a statistical or data analysis.

( b ) Although the scale may display 0, this does not necessarily indicate the absence or true zero. For instance, a zero on a personality test does not necessarily indicate that the test-taker is completely lacking in the attribute being assessed.

( c ) Values between two variables might be subtracted to comprehend how they differ from one another. For instance, when we measure temperature (in Fahrenheit), the distance between 45 and 55 equals the distance between 65 and 75. 

( d ) The mean, median, and mode of a set of variables can be calculated using interval measurement. The mean is the data set’s average, the median is the middle, and the mode is the most frequent data.

( e ) You cannot learn about proportion using data on an interval scale; you can only learn about order and difference. The ratio between two values cannot be measured using an interval scale. A value’s data cannot be divided or multiplied by another value.

( 4 ) Ratio

The definition of a ratio scale is a variable measurement scale that not only determines the order of the variables but also reveals the differences between them and provides information on the value of true zero. It is determined by making the assumptions that each variable has a zero choice, that the difference between each variable is the same, and that the options are in a particular order.

Examples of Ratio Scales

Some examples of ratio data include age, height, weight, speed in miles per hour, population, etc. 

Characteristics of Ratio Scales

The ratio scales have the following characteristics:

( a ) There is a true zero point, and you may categorize, rank, and infer equal distances between nearby data points.

( b ) Zero does signify a complete absence of the variable in ratio scales. A true zero indicates the lack of the relevant variable. For instance, if we are discussing population, it is understood that there are no people if the population count is zero.

( c ) You can calculate ratios of the numbers on ratio scales since they have a true zero. For instance, a class with a population of twenty persons can be compared to one with a population of forty as being half the size.

( d ) Ratio scales have all the characteristics of the interval scales along with the presence of the true zero value.

( e ) The ratio scale can be used to compute the mean, median, and mode of a set of data, which are all measures of central tendency.

Importance of Levels of Measurement

It is essential to note that the level of measurement determines the kind of statistical analysis you may perform. It consequently influences the type and extent of insights you can draw from your data. It is essential to decide in advance how you’ll collect and measure your data because some statistical tests can only be run where more exact levels of measurement have been employed.

The various levels place restrictions on the kind of inferential statistics you can run on your data to confirm or disprove your hypothesis, as well as the descriptive statistics you can use to obtain a broad overview of your data.

Your variables can frequently be assessed at several levels; therefore, before you start gathering data, you must decide which level of measurement you will apply.

More Examples

Identify the level of measurement displayed in each of the following cases. 

( a ) A researcher gathers demographic information from her participants. She asks about the participants’ birthplaces.

( b ) A group of students conducts their research and asks their participants about the number of hours they spent going to work. 

( c ) A researcher collects data from his participants using a personality test. In this exam, a score of zero indicates a low level of the attribute being measured.

( d ) The customers were asked about their satisfaction with the service in a survey. They must select whether the service was very poor, poor, average, good, or excellent.

Answers

( a ) Nominal Scale. Cities can be categorized, and there is no natural order. Hence birthplaces are only nominal.

( b ) Ratio Scale. The number of hours is a ratio scale since there exist equal intervals and true zero.

( c ) Interval Scale. The scale of personality tests administered can be ordered, and there are equal intervals. This cannot be a ratio scale since there is no true zero since the 0 score means low of the measured attribute. 

( d ) Ordinal. Customer level satisfaction is ordinal since it has natural rank order.

Summary

Levels of Measurement

The level of measurement is crucial because it affects the kind of statistical analysis you can run. A variable’s level of measurement describes how precisely it has been measured.

There are four types of measurement: nominal, ordinal, ratio, and ordinal.

The least amount of information is included in nominal scales. A nominal scale is the most basic measurement system we may use to name variables. Variables without quantitative values are labeled using a nominal scale. A nominal scale is a naming scale where variables are merely “named” or labeled with no particular order.

Some examples of nominal scales are gender, eye color, marital status, hair color, blood type, etc.

Variables with a natural order but no quantitative difference in values are labeled using the ordinal scale. Ordinal scales are a higher degree of measurement since they provide more information than nominal scales.

Some examples of ordinal scales are the degree of pain, economic status, customer satisfaction level, etc.

Variables with the natural order, measurable differences between values, but no true zero value are characterized by interval scale. Because they guarantee that there are no significant differences between values, interval scales provide more information than ordinal scales. In other words, interval scales are ordinal scales with equivalent scale values across the range of intervals from low to high.

Some examples of interval scales are personal inventories, test scores, family income, the temperature measured in Celsius or Fahrenheit, etc.

The definition of a ratio scale is a variable measurement scale that not only determines the order of the variables but also reveals the differences between them and provides information on the value of true zero. It is determined by making the assumptions that each variable has a zero choice, that the difference between each variable is the same, and that the options are in a particular order.

Some examples of ratio data include age, height, weight, speed in miles per hour, population, etc. 

Frequently Asked Questions on Levels of Measurement (FAQs)

Why are the levels of measurement important?

It is essential to note that the level of measurement determines the kind of statistical analysis you may perform. It consequently influences the type and extent of insights you can draw from your data. It is essential to decide in advance how you’ll collect and measure your data because some statistical tests can only be run where more exact levels of measurement have been employed.

The various levels place restrictions on the kind of inferential statistics you can run on your data to confirm or disprove your hypothesis, as well as the descriptive statistics you can use to obtain a broad overview of your data.

Your variables can frequently be assessed at several levels; therefore, before you start gathering data, you must decide which level of measurement you will apply.

What are the four levels of measurement, and how do we differentiate them?

There are four types of measurement: nominal, ordinal, ratio, and ordinal.

The least amount of information is included in nominal scales. A nominal scale is the most basic measurement system we may use to name variables. Variables without quantitative values are labeled using a nominal scale. A nominal scale is a naming scale where variables are merely “named” or labeled with no particular order.

Variables with a natural order but no quantitative difference in values are labeled using the ordinal scale. Ordinal scales are a higher degree of measurement since they provide more information than nominal scales.

Variables with the natural order, measurable differences between values, but no true zero value are characterized by interval scale. Because they guarantee that there are no significant differences between values, interval scales provide more information than ordinal scales. In other words, interval scales are ordinal scales with equivalent scale values across the range of intervals from low to high.

The definition of a ratio scale is a variable measurement scale that not only determines the order of the variables but also reveals the differences between them and provides information on the value of true zero. It is determined by making the assumptions that each variable has a zero choice, that the difference between each variable is the same, and that the options are in a particular order.

The table below shows the characteristics, central tendency measures, and examples of each measurement level.

Levels of MeasurementCharacteristicsCentral Tendency MeasureExamples
NominalCategoriesModeGender, Blood Type, Hair Color, Marital Status
OrdinalRankings Median and ModeLevels of Pain, Customer Level Satisfaction
IntervalDifferences between measurements (no true zero)Mean, Median, and ModeTemperature (Celsius or Fahrenheit) Personal InventoriesTest Scores
RatioDifferences between measurements and true zero existMean, Median, and ModeAge, Height, Weight

How do we use the four levels of measurement in research and statistics?

Nominal, ordinal, interval and ratio measurements are the four types of measurements used in statistics and research. The nominal scale does not indicate a numerical value or rank and is used to designate variables in various classifications. For non-mathematical concepts like frequency, satisfaction, happiness, level of pain, etc., the ordinal scale is utilized. The interval scale is used to display both the difference between the variables and their order. The ratio scale generates information about the value of the true zero as well as the difference between known variables in addition to the order of the variables.

What measures of central tendency can be calculated using four levels of measurement?

It depends on the levels of measurement and what kind of statistical analysis you could do. A variable’s level of measurement describes how precisely it has been measured. From the data set, mean, median, and mode are three central tendency measures that can be computed. The mean is the data set’s average, the median is the middle value, and the mode is the variable that occurred most frequently.

The interval and ratio scales can be used to compute the mean, median, and mode of a data set, all measures of central tendency. In ordinal scales, both median and mode can be calculated. Only the mode can be calculated in nominal scales. 

What is true zero in levels of measurement?

A true zero indicates the lack of the relevant variable. Zero does signify a complete absence  of the variable in ratio scales.

For instance, there are no negative degrees of temperature on the Kelvin temperature scale because zero denotes a complete absence of thermal energy.

The scales for weight, height, time, and calories are other instances of scales with a true zero.

What is the difference between nominal scale and ordinal scale?

The least amount of information is included in nominal scales. A nominal scale is the most basic measurement system we may use to name variables. Variables without quantitative values are labeled using a nominal scale. A nominal scale is a naming scale where variables are merely “named” or labeled with no particular order.

Variables with a natural order but no quantitative difference in values are labeled using the ordinal scale. Ordinal scales are a higher degree of measurement since they provide more information than nominal scales.

What distinguishes the interval scale from the ratio scale?

Variables with the natural order, measurable differences between values, but no true zero value are characterized by interval scale. Because they guarantee that there are no significant differences between values, interval scales provide more information than ordinal scales. In other words, interval scales are ordinal scales with equivalent scale values across the range of intervals from low to high.The definition of a ratio scale is a variable measurement scale that not only determines the order of the variables but also reveals the differences between them and provides information on the value of true zero. It is determined by making the assumptions that each variable has a zero choice, that the difference between each variable is the same, and that the options are in a particular order.

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