# 2.2: Scales of Measurement (2023)

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As the previous section indicates, the outcome of a psychological measurement is called a variable. But not all variables are of the same qualitative type, and it’s very useful to understand what types there are. A very useful concept for distinguishing between different types of variables is what’s known as scales of measurement.

## Nominal scale

A nominal scale variable (also referred to as a categorical variable) is one in which there is no particular relationship between the different possibilities: for these kinds of variables it doesn’t make any sense to say that one of them is “bigger’ or”better" than any other one, and it absolutely doesn’t make any sense to average them. The classic example for this is “eye colour”. Eyes can be blue, green and brown, among other possibilities, but none of them is any “better” than any other one. As a result, it would feel really weird to talk about an “average eye colour”. Similarly, gender is nominal too: male isn’t better or worse than female, neither does it make sense to try to talk about an “average gender”. In short, nominal scale variables are those for which the only thing you can say about the different possibilities is that they are different. That’s it.

Let’s take a slightly closer look at this. Suppose I was doing research on how people commute to and from work. One variable I would have to measure would be what kind of transportation people use to get to work. This “transport type” variable could have quite a few possible values, including: “train”, “bus”, “car”, “bicycle”, etc. For now, let’s suppose that these four are the only possibilities, and suppose that when I ask 100 people how they got to work today, and I get this:

 Transportation Number of people (1) Train 12 (2) Bus 30 (3) Car 48 (4) Bicycle 10

So, what’s the average transportation type? Obviously, the answer here is that there isn’t one. It’s a silly question to ask. You can say that travel by car is the most popular method, and travel by train is the least popular method, but that’s about all. Similarly, notice that the order in which I list the options isn’t very interesting. I could have chosen to display the data like this

 Transportation Number of people (3) Car 48 (1) Train 12 (4) Bicycle 10 (2) Bus 30

and nothing really changes.

(Video) Measurement Scales (Nominal, Ordinal, Interval, Ratio) - Statistics

## Ordinal scale

Ordinal scale variables have a bit more structure than nominal scale variables, but not by a lot. An ordinal scale variable is one in which there is a natural, meaningful way to order the different possibilities, but you can’t do anything else. The usual example given of an ordinal variable is “finishing position in a race”. You can say that the person who finished first was faster than the person who finished second, but you don’t know how much faster. As a consequence we know that 1st > 2nd, and we know that 2nd > 3rd, but the difference between 1st and 2nd might be much larger than the difference between 2nd and 3rd.

Here’s an more psychologically interesting example. Suppose I’m interested in people’s attitudes to climate change, and I ask them to pick one of these four statements that most closely matches their beliefs:

1. Temperatures are rising, because of human activity
2. Temperatures are rising, but we don’t know why
3. Temperatures are rising, but not because of humans
4. Temperatures are not rising

Notice that these four statements actually do have a natural ordering, in terms of “the extent to which they agree with the current science”. Statement 1 is a close match, statement 2 is a reasonable match, statement 3 isn’t a very good match, and statement 4 is in strong opposition to the science. So, in terms of the thing I’m interested in (the extent to which people endorse the science), I can order the items as 1 > 2 > 3 > 4. Since this ordering exists, it would be very weird to list the options like this…

1. Temperatures are rising, but not because of humans
2. Temperatures are rising, because of human activity
3. Temperatures are not rising
4. Temperatures are rising, but we don’t know why

… because it seems to violate the natural “structure” to the question.

So, let’s suppose I asked 100 people these questions, and got the following answers:

 Response Number (1) Temperatures are rising, because of human activity 51 (2) Temperatures are rising, but we don’t know why 20 (3) Temperatures are rising, but not because of humans 10 (4) Temperatures are not rising 19

When analysing these data, it seems quite reasonable to try to group (1), (2) and (3) together, and say that 81 of 100 people were willing to at least partially endorse the science. And it’s also quite reasonable to group (2), (3) and (4) together and say that 49 of 100 people registered at least some disagreement with the dominant scientific view. However, it would be entirely bizarre to try to group (1), (2) and (4) together and say that 90 of 100 people said… what? There’s nothing sensible that allows you to group those responses together at all.

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That said, notice that while we can use the natural ordering of these items to construct sensible groupings, what we can’t do is average them. For instance, in my simple example here, the “average” response to the question is 1.97. If you can tell me what that means, I’d love to know. Because that sounds like gibberish to me!

## Interval scale

In contrast to nominal and ordinal scale variables, interval scale and ratio scale variables are variables for which the numerical value is genuinely meaningful. In the case of interval scale variables, the differences between the numbers are interpretable, but the variable doesn’t have a “natural” zero value. A good example of an interval scale variable is measuring temperature in degrees celsius. For instance, if it was 15o yesterday and 18∘ today, then the 3o difference between the two is genuinely meaningful. Moreover, that 3o difference is exactly the same as the 3o difference between 7o and 10o. In short, addition and subtraction are meaningful for interval scale variables.8

However, notice that the 0o does not mean “no temperature at all”: it actually means “the temperature at which water freezes”, which is pretty arbitrary. As a consequence, it becomes pointless to try to multiply and divide temperatures. It is wrong to say that 20o is twice as hot as 10o, just as it is weird and meaningless to try to claim that 20o is negative two times as hot as -10o.

Again, lets look at a more psychological example. Suppose I’m interested in looking at how the attitudes of first-year university students have changed over time. Obviously, I’m going to want to record the year in which each student started. This is an interval scale variable. A student who started in 2003 did arrive 5 years before a student who started in 2008. However, it would be completely insane for me to divide 2008 by 2003 and say that the second student started “1.0024 times later” than the first one. That doesn’t make any sense at all.

## Ratio scale

The fourth and final type of variable to consider is a ratio scale variable, in which zero really means zero, and it’s okay to multiply and divide. A good psychological example of a ratio scale variable is response time (RT). In a lot of tasks it’s very common to record the amount of time somebody takes to solve a problem or answer a question, because it’s an indicator of how difficult the task is. Suppose that Alan takes 2.3 seconds to respond to a question, whereas Ben takes 3.1 seconds. As with an interval scale variable, addition and subtraction are both meaningful here. Ben really did take 3.1 - 2.3 = 0.8 seconds longer than Alan did. However, notice that multiplication and division also make sense here too: Ben took 3.1 / 2.3 = 1.35 times as long as Alan did to answer the question. And the reason why you can do this is that, for a ratio scale variable such as RT, “zero seconds” really does mean “no time at all”.

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## Continuous versus discrete variables

There’s a second kind of distinction that you need to be aware of, regarding what types of variables you can run into. This is the distinction between continuous variables and discrete variables. The difference between these is as follows:

• A continuous variable is one in which, for any two values that you can think of, it’s always logically possible to have another value in between.
• A discrete variable is, in effect, a variable that isn’t continuous. For a discrete variable, it’s sometimes the case that there’s nothing in the middle.

These definitions probably seem a bit abstract, but they’re pretty simple once you see some examples. For instance, response time is continuous. If Alan takes 3.1 seconds and Ben takes 2.3 seconds to respond to a question, then it’s possible for Cameron’s response time to lie in between, by taking 3.0 seconds. And of course it would also be possible for David to take 3.031 seconds to respond, meaning that his RT would lie in between Cameron’s and Alan’s. And while in practice it might be impossible to measure RT that precisely, it’s certainly possible in principle. Because we can always find a new value for RT in between any two other ones, we say that RT is continuous.

Discrete variables occur when this rule is violated. For example, nominal scale variables are always discrete: there isn’t a type of transportation that falls “in between” trains and bicycles, not in the strict mathematical way that 2.3 falls in between 2 and 3. So transportation type is discrete. Similarly, ordinal scale variables are always discrete: although “2nd place” does fall between “1st place” and “3rd place”, there’s nothing that can logically fall in between “1st place” and “2nd place”. Interval scale and ratio scale variables can go either way. As we saw above, response time (a ratio scale variable) is continuous. Temperature in degrees celsius (an interval scale variable) is also continuous. However, the year you went to school (an interval scale variable) is discrete. There’s no year in between 2002 and 2003. The number of questions you get right on a true-or-false test (a ratio scale variable) is also discrete: since a true-or-false question doesn’t allow you to be “partially correct”, there’s nothing in between 5/10 and 6/10. Table 2.1 summarises the relationship between the scales of measurement and the discrete/continuity distinction. Cells with a tick mark correspond to things that are possible. I’m trying to hammer this point home, because (a) some textbooks get this wrong, and (b) people very often say things like “discrete variable” when they mean “nominal scale variable”. It’s very unfortunate.

Table 2.1: The relationship between the scales of measurement and the discrete/continuity distinction. Cells with a tick mark correspond to things that are possible.

 continuous discrete nominal ✓ ordinal ✓ interval ✓ ✓ ratio ✓ ✓

## Some complexities

Okay, I know you’re going to be shocked to hear this, but … the real world is much messier than this little classification scheme suggests. Very few variables in real life actually fall into these nice neat categories, so you need to be kind of careful not to treat the scales of measurement as if they were hard and fast rules. It doesn’t work like that: they’re guidelines, intended to help you think about the situations in which you should treat different variables differently. Nothing more.

(Video) 2.2 Units of Measurement & Metric Conversions

So let’s take a classic example, maybe the classic example, of a psychological measurement tool: the Likert scale. The humble Likert scale is the bread and butter tool of all survey design. You yourself have filled out hundreds, maybe thousands of them, and odds are you’ve even used one yourself. Suppose we have a survey question that looks like this:

Which of the following best describes your opinion of the statement that “all pirates are freaking awesome” …

and then the options presented to the participant are these:

(1) Strongly disagree
(2) Disagree
(3) Neither agree nor disagree
(4) Agree
(5) Strongly agree

This set of items is an example of a 5-point Likert scale: people are asked to choose among one of several (in this case 5) clearly ordered possibilities, generally with a verbal descriptor given in each case. However, it’s not necessary that all items be explicitly described. This is a perfectly good example of a 5-point Likert scale too:

(1) Strongly disagree
(2)
(3)
(4)
(5) Strongly agree

Likert scales are very handy, if somewhat limited, tools. The question is, what kind of variable are they? They’re obviously discrete, since you can’t give a response of 2.5. They’re obviously not nominal scale, since the items are ordered; and they’re not ratio scale either, since there’s no natural zero.

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But are they ordinal scale or interval scale? One argument says that we can’t really prove that the difference between “strongly agree” and “agree” is of the same size as the difference between “agree” and “neither agree nor disagree”. In fact, in everyday life it’s pretty obvious that they’re not the same at all. So this suggests that we ought to treat Likert scales as ordinal variables. On the other hand, in practice most participants do seem to take the whole “on a scale from 1 to 5” part fairly seriously, and they tend to act as if the differences between the five response options were fairly similar to one another. As a consequence, a lot of researchers treat Likert scale data as if it were interval scale. It’s not interval scale, but in practice it’s close enough that we usually think of it as being quasi-interval scale.

## FAQs

### 2.2: Scales of Measurement? ›

Psychologist Stanley Stevens developed the four common scales of measurement: nominal, ordinal, interval and ratio. Each scale of measurement has properties that determine how to properly analyse the data. The properties evaluated are identity, magnitude, equal intervals and a minimum value of zero.

What are the 4 measurement scales with examples? ›

Psychologist Stanley Stevens developed the four common scales of measurement: nominal, ordinal, interval and ratio. Each scale of measurement has properties that determine how to properly analyse the data. The properties evaluated are identity, magnitude, equal intervals and a minimum value of zero.

What is a measurement scale that rates product quality as either 1 poor 2 average and 3 good is known as? ›

A measurement scale that rates product quality as either 1 = poor, 2 = average, and 3 = good is known as. nominal.

What is an example of scale measurement? ›

The best examples of ratio scales are weight and height. In market research, a ratio scale is used to calculate market share, annual sales, the price of an upcoming product, the number of consumers, etc.

What are normal measurement scales? ›

A Nominal Scale is a measurement scale, in which numbers serve as “tags” or “labels” only, to identify or classify an object. This measurement normally deals only with non-numeric (quantitative) variables or where numbers have no value.

What is an example of ordinal scale of measurement? ›

Ordinal Examples

A student scoring 99/100 would be the 1st rank, another student scoring 92/100 would be 3rd and so on and so forth.

What are the 4 types of scales and discuss each type? ›

Each of the four scales (i.e., nominal, ordinal, interval, and ratio) provides a different type of information. Measurement refers to the assignment of numbers in a meaningful way, and understanding measurement scales is important to interpreting the numbers assigned to people, objects, and events.

What is simplest level of measurement? ›

The nominal level of measurement is the simplest level. "Nominal" means "existing in name only." With the nominal level of measurement all we can do is to name or label things. Even when we use numbers, these numbers are only names.

Which of the following is an example of ratio scale level of measurement? ›

Length, area, and population are examples of ratio scales.

What is the least scale of measurement? ›

The nominal measurement scale is the lowest level of measurement in statistics and therefore has the lowest information content. Possible values of the variables can be distinguished, but a meaningful order is not possible.

### What are the three types of scale and examples? ›

There are three types of scales commonly used on maps: written or verbal scale, a graphic scale, or a fractional scale. A written or verbal scale uses words to describe the relationship between the map and the landscape it depicts such as one inch represents one mile.

How do you find the scale measure? ›

How do you Find the Scale Factor? The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

What is the best scale of measurement? ›

Ratio scales

Ratio scales are the most informative scales. Ratio scales provide rankings, assure equal differences between scale values, and have a true zero point.

What is the most accurate measurement scale? ›

The ratio scale is called the highest scale in measurement. It is the most reliable scale of measurement. It carries all the characteristics of earlier discussed scales with a true or absolute zero point.

How do I choose a scale? ›

I like to give students the following tips when demonstrating selecting an appropriate scale:
1. Try to make the graph fill most of the space, using a break in the axis scale if appropriate. ...
2. To make the divisions on an axis easy to plot, factors of two or five are probably best.
Sep 5, 2018

What is an example of interval scale? ›

An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).

What is the example of nominal scale? ›

Example of Nominal Scale

Gender, marital status, religion, race, hair color, country, etc are examples of Nominal Scale. They are all examples of nouns that do not require rank or order.

What is the example of nominal? ›

Nominal data are used to label variables without any quantitative value. Common examples include male/female (albeit somewhat outdated), hair color, nationalities, names of people, and so on. In plain English: basically, they're labels (and nominal comes from "name" to help you remember).

What is an example of interval and ratio? ›

Examples of interval level data include temperature and year. Examples of ratio level data include distance and area (e.g., acreage).

Is age an ordinal data? ›

Age can be both nominal and ordinal data depending on the question types. I.e “How old are you” is used to collect nominal data while “Are you the firstborn or What position are you in your family” is used to collect ordinal data. Age becomes ordinal data when there's some sort of order to it.

### What level of measurement is GPA? ›

High schools often report GPA (grade point average) on a 4.0 scale. The top grade is an A, which equals 4.0. You calculate your overall GPA by averaging the scores of all your classes. This is a common scale used at most colleges, and many high schools also use it.

What scale of measurement is age? ›

Age, money, and weight are common ratio scale variables. For example, if you are 50 years old and your child is 25 years old, you can accurately claim you are twice their age.

What level of measurement is yes or no? ›

Data that is measured using a nominal scale is qualitative (categorical). Categories, colors, names, labels, favorite foods, and 'yes' or 'no' responses are examples of nominal level data.

What is an example of ordinal data? ›

For example, first, second, and third places in a race are ordinal data. You can clearly understand the order of finishes. However, the time difference between first and second place might not be the same as between second and third place. Ordinal data are prevalent in social science and survey research.

What is an example of a ratio? ›

For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).

What is an example of a ratio level? ›

The most common examples of this scale are height, money, age, weight etc. With respect to market research, the common examples that are observed are sales, price, number of customers, market share etc.

What is the weakest and simplest scale of measurement? ›

Nominal or Categorical Scale

The simplest, most basic, and weakest type of measurement is when we can replace real objects with symbols or numbers (without understanding their numerical meanings).

What is the weakest to strongest measurement scale? ›

The order of the traditional measurement scales presented above—nominal, then ordinal, then interval, then ratio—is from weakest to strongest in terms of statistical inference.

What is the most smallest measurement? ›

Some Interesting Facts:
• The smallest length with any meaning is the Planck length (about 1.6 x 10-35 meter)
• Quarks are very very small (less than 10-19 meters)
• A Hydrogen atom is about 100 picometers in diameter (1.06 x 10-10 meters)
• Molecules are around the billionths of a meter in size.

Which is an example of which scale? ›

For example, a scale of 1:5 means that the size of 1 unit in the drawing would represent 5 units in the real world. For example, if a giraffe with a height of 150 inches in the real world is represented as 30 inches on the drawing, it shows that a scale of 1:5 is used.

### What are the three commonly used scales? ›

What does scale 3 mean? ›

For example, scale factor 3 means that the new shape is thrice the size of the original shape.

What are the 2 types of measurement? ›

The two systems used for specifying units of measure are the English and metric systems.

What is a measurement answer? ›

Measurement is a comparison of an unknown quantity with a known fixed quantity of the same kind. The value obtained on measuring a quantity is called its magnitude. The magnitude of a quantity is expressed in numbers and in its unit.

What are the basic measurements? ›

SI Base Units
QuantitySI Base Unit
Lengthmeterm
Masskilogramkg
TemperaturekelvinK
Timeseconds
3 more rows
Sep 3, 2019

What is the scale factor of 2? ›

If you have a "number n" (n), a "number n prime" (n′) and a Scale Factor of 2, then it means the following: n × 2 = n′ In other words per the equation above, a Scale Factor of 2 is the factor that you would multiply with n to get n′.

What are examples of scale models? ›

Maps, house plans, and biology cell drawings are examples of items that use scale drawings. When using a model, scale factor is always the ratio of the model's dimensions to the actual object's dimensions.

What are the 4 types of measurement? ›

You can see there are four different types of measurement scales (nominal, ordinal, interval and ratio). Each of the four scales, respectively, typically provides more information about the variables being measured than those preceding it.

What is a scale in a questionnaire? ›

A survey scale represents a set of answer options (either numeric or verbal) that cover a range of opinions on a topic. It's always part of a closed-ended question (a question that presents respondents with pre-populated answer choices).

Why a scale of 1 to 5 is better? ›

Many people prefer the 1 to 5 rating scale since it's simple and easily understood. Rating something on a 1 to 5 scale provides a good range, from mild to severe, so that people can get an idea of how bad a problem is. It's also easier to compare things that have been rated on the same scale.

### Which scale is most accurate and why? ›

The Etekcity EB9380H is one of the most accurate and precise digital bathroom scales we've tested. Many inexpensive bathroom scales respond reliably only to a weight change on the order of half a pound, or, as we found through our testing, will even pull your weight readings from memory without trying to measure you.

How do you measure scale accuracy? ›

The accuracy of a scale is a measure of the degree of closeness of the average value of an object's displayed weight to the object's actual weight. If, on average, a scale indicates that a 200 lb reference weight weighs 200.20 lb, then the scale is accurate to within 0.20 lb in 200 lb, or 0.1%.

Why does my scales say 2 different weights? ›

That's because each brand of scale may have different calibrations, and some scales may be synchronized for your own body type or BMI. If they're good scales, they'll probably get an accurate reading that's very close to your correct body weight.

Which scale is best for beginners? ›

What scale should I learn first? Well the most common scale to learn first is the Minor Pentatonic Scale. That's the one that I recommend that you start with and it is included in my beginners course. Once you have that one down (and can use it) then you should explore the Major Scale.

What scales should beginners learn? ›

Minor pentatonic scale

This is by far the most versatile scale out there and the one most people learn first. You can think of the minor pentatonic scale as the one that'll be your safety net for any kind of improvisation you need to perform at any given time.

What does 2cm to 1 unit mean? ›

It could denote and represent one unit on both axes and coordinates of the vertices are meeting at same line. This represents one unit on the t-axis across the paper and 2cm to represent in one unit.

What is an example of an interval scale? ›

An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).

What are the four 4 levels or scales of measurement? ›

Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.

What is an example of interval vs ratio? ›

Examples of interval level data include temperature and year. Examples of ratio level data include distance and area (e.g., acreage). The scales are similar in so far as units of measurement are arbitrary (Celsius versus Fahrenheit, Gregorian versus Islamic calendar, English versus metric units).

What is basic 4 measurement? ›

The standard unit for measurement of length is meter. Apart from the meter, we have various units such as a meter, kilometer, millimeter, feet, inches, and so on. Meter is also called the SI unit of length or base unit of length.

### What is nominal scale with example? ›

Example of Nominal Scale

Gender, marital status, religion, race, hair color, country, etc are examples of Nominal Scale. They are all examples of nouns that do not require rank or order.

What is a ordinal question? ›

What is an ordinal survey question? An ordinal scale survey question asks survey participants to rate their opinion, experience, or agreement on a scale that has a specific order. In the ordinal scale, however, the responses don't have consistent distance. A common example of an ordinal scale is the Likert Scale.

What is an example of an ordinal question? ›

This popular form of survey question offers respondents an ordered range of answers from one extreme to another. Take, for example, these questions from our Employee Satisfaction Survey Template: How meaningful is your work? How challenging is your job?

What is an example of ratio data? ›

Income, height, weight, annual sales, market share, product defect rates, time to repurchase, unemployment rate, and crime rate are examples of ratio data.

What is the 4 level ordinal scale? ›

These four categories correspond to an objective score as follows: Superior – 90 to 100; Effective – 70 to 89; Minimal – 40 to 69; Inadequate – 0 to 39. Even though the four categories were determined by a score from 1 to 100, the categories themselves are measured at the ordinal level.

Is weight a ratio or interval? ›

A weight of 4 grams is twice a weight of 2 grams, because weight is a ratio variable.

Is time an interval or ratio? ›

Time and duration are two examples of interval and ratio scale respectively. Time is the value of the interval scale because there is no zero. You cannot tell when time started. Duration is a case of ratio scale for the fact that duration has a starting point.

Is blood pressure an interval or ratio? ›

Answer and Explanation: Clearly, this variable makes use of two values, and the difference between them tells us if we have normal or high blood pressure. Because of this, systolic blood pressure can be classified as an interval variable.

Is Age A nominal or interval? ›

Age can be both nominal and ordinal data depending on the question types. I.e “How old are you” is used to collect nominal data while “Are you the firstborn or What position are you in your family” is used to collect ordinal data. Age becomes ordinal data when there's some sort of order to it.

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