Are Interval and Ratio Variables Continuous

Measurement variables, or simply variables are commonly used in different physical science fields—including mathematics, computer science, and statistics. It has a different meaning and application in each of these fields.

In algebra, which is a common aspect of mathematics, a variable is simply referred to as an unknown value. This meaning is what is adopted in computer science, where it is used to define values when writing in various computer programming languages.

However, variables have a slightly different meaning and use in statistics. Although it also slightly intersects with algebraic meaning, its uses and definition differ greatly.

What is a Measurement Variable?

A measurement variable is an unknown attribute that measures a particular entity and can take one or more values. It is commonly used for scientific research purposes. Unlike in mathematics, measurement variables can not only take quantitative values but can also take qualitative values in statistics.

Statistical variables can be measured using measurement instruments, algorithms, or even human discretion.

How we measure variables are called scale of measurements, and it affects the type of analytical techniques that can be used on the data, and conclusions that can be drawn from it. Measurement variables are categorized into four types, namely; nominal, ordinal, interval and ratio variables.

Types of Measurement Variables

Nominal Variable

A nominal variable is a type of variable that is used to name, label or categorize particular attributes that are being measured. It takes qualitative values representing different categories, and there is no intrinsic ordering of these categories.

You can code nominal variables with numbers, but the order is arbitrary and arithmetic operations cannot be performed on the numbers. This is the case when a person's phone number, National Identification Number postal code, etc. are being collected.

A nominal variable is one of the 2 types of categorical variables and is the simplest among all the measurement variables. Some examples of nominal variables include gender, Name, phone, etc.

nominal-variables

Types of Nominal Variable

In statistics, there is no standard classification of nominal variables into types. However, we can classify them into different types based on some factors. We will be considering 2 factors in this case, namely; collection technique and numeric property.

Nominal Variable Classification Based on Collection Technique

There are different methods of collecting nominal variables, which may vary according to the purpose of collecting nominal data in the first place. Some of these methods include surveys, questionnaires, interviews, etc.

It doesn't matter which method is used for data collection, one thing is however common to these methods—they are implemented using questions. The respondents are either asked, open-ended or closed-ended.

Open-ended

The open-ended technique gives respondents the freedom to respond the way they like. They are allowed to freely express their emotions.

This technique is used to collect detailed and descriptive information. For example, an organization who wants to receive feedback from its customers may ask, "How do you think we can improve our service?"—where the question asked is the nominal variable.

Closed-ended

This technique restricts the kind of response a respondent can give to the questions asked. Questionnaires give predefined options for the respondent to choose from.

Unlike open-ended, this technique collects data from the questionnaire's point of view, thereby limiting the respondent's freedom. A closed-ended approach to the question asked above will be

How do you think we can improve our service?

New menu
Better design
Train chefs
More attractive plating

Nominal Variable Classification Based on Numeric Property

Nominal variables are sometimes numeric but do not possess numerical characteristics. Some of thee numeric nominal variables are; phone numbers, student numbers, etc.

Therefore, a nominal variable can be classified as either numeric or not.

Characteristics of Nominal Variable

The responses to a nominal variable can be divided into two or more categories. For example, gender is a nominal variable that can take responses male/female, which are the categories the nominal variable is divided into.
A nominal variable is qualitative, which means numbers are used here only to categorize or identify objects. For example, the number at the back of a player's jersey is used to identify the position he/she is playing.
They can also take quantitative values. However, these quantitative values do not have numeric properties. That is, arithmetic operations cannot be performed on them.

Examples of Nominal Variable

Personal Biodata: The variables included in a personal biodata is a nominal variable. This includes the name, date of birth, gender, etc. E.g
Full Name _____
Gender
Email address_____
Customer Feedback: Organizations use this to get feedback about their product or service from customers. E.g.

How long have you been using our product?

Less than 6 months
6 months
7 months+
What do you think about our mobile app?_____

Categories of Nominal Variable

There are 2 main categories of nominal variables, namely; the matched and unmatched categories.

The Matched Category: In this category, all the values of the nominal variable are paired up or grouped so that each member of a group has similar characteristics except for the variable under investigation.
The Unmatched Category: This is an independent sample of unrelated groups of data. Unlike in the matched category, the values in a group do not necessarily have similar characteristics.

Ordinal Variable

An ordinal variable is a type of measurement variable that takes values with an order or rank. It is the 2nd level of measurement and is an extension of the nominal variable.

They are built upon nominal scales by assigning numbers to objects to reflect a rank or ordering on an attribute. Also, there is no standard ordering in the ordinal variable scale.

In another sense, we could say the difference in the rank of an ordinal variable is not equal. It is mostly classified as one of the 2 types of categorical variables, while in some cases it is said to be a midpoint between categorical and numerical variables.

Types of Ordinal Variable

Similar to the nominal variable, there is no standard classification of ordinal variables into types. However, we will be classifying them according to the value assignment. I.e. Ordinal Variable type based on numerical and non numerical values.

What do we mean by value assignment?

The possible values of ordinal variables do have a rank or order, and a numeric value may be assigned to each rank for respondents to better understand them. In other cases, numeric values are not assigned to the ranks.

Below are examples of ordinal variable with and without numeric value.

Ordinal Variable With Numeric Value

How satisfied are you with our service tonight?

Very satisfied
Satisfied
Indifferent
Dissatisfied
Very dissatisfied

Ordinal Variable Without Numeric value

How satisfied are you with our service tonight?

Very satisfied
Satisfied
Indifferent
Dissatisfied
Very dissatisfied

Characteristics of Ordinal Variable

It is an extension of nominal data.
It has no standardized interval scale.
It establishes a relative rank.
It measures qualitative traits.
The median and mode can be analyzed.
It has a rank or order.

Examples of Ordinal Variable

Likert Scale: A Likert scale is a psychometric scale used by researchers to prepare questionnaires and get people's opinions.

How satisfied are you with our service?

Very satisfied
Satisfied
Indifferent
Dissatisfied
Very dissatisfied

Interval Scale: each response in an interval scale is an interval on its own.

How old are you?

13-19 years
20-30 years
31-50 years

Categories of Ordinal Variable

There are also 2 main categories of ordinal variables, namely; the matched and unmatched category.

The Matched Category: In the matched category, each member of a data sample is paired with similar members of every other sample concerning all other variables, aside from the one under consideration. This is done to obtain a better estimation of differences.
The Unmatched Category: Unmatched category, also known as the independent category contains randomly selected samples with variables that do not depend on the values of other ordinal variables. Most researchers base their analysis on the assumption that the samples are independent, except in a few cases.

Differences Between Nominal and Ordinal Variable

The ordinal variable has an intrinsic order while nominal variables do not have an order.
It is only the mode of a nominal variable that can be analyzed while analysis like the median, mode, quantile, percentile, etc. can be performed on ordinal variables.
The tests carried on nominal and ordinal variables are different.

Similarities Between Nominal and Ordinal Variable

They are both types of categorical variables.
They both have an inconclusive mean and a mode.
They are both visualized using bar charts and pie charts.

Interval Variable

The interval variable is a measurement variable that is used to define values measured along a scale, with each point placed at an equal distance from one another. It is one of the 2 types of numerical variables and is an extension of the ordinal variable.

Unlike ordinal variables that take values with no standardized scale, every point in the interval scale is equidistant. Arithmetic operations can also be performed on the numerical values of the interval variable.

These arithmetic operations are, however, just limited to addition and subtraction. Examples of interval variables include; temperature measured in Celsius or Fahrenheit, time, generation age range, etc.

interval-variable

Characteristics of Interval Variable

It is one of the 2 types of quantitative variables. It takes numeric values and may be classified as a continuous variable type.
Arithmetic operations can be performed on interval variables. However, these operations are restricted to only addition and subtraction.
The interval variable is an extension of the ordinal variable. In other words, we could say interval variables are built upon ordinary variables.
The intervals on the scale are equal in an interval variable. The scale is equidistant.
The variables are measured using an interval scale, which not only shows the order but also shows the exact difference in the value.
It has no zero value.

Examples of Interval Variable

Temperature: Temperature, when measured in Celsius or Fahrenheit is considered as an interval variable.
Mark Grading: When grading test scores like the SAT, for example, we use numbers as a reference point.
Time: Time, if measured using a 12-hour clock, or it is measured during the day is an example of interval data.
IQ Test: An individual cannot have a zero IQ, therefore satisfying the no zero property of an interval variable. The level of an individual's IQ will be determined, depending on which interval the score falls in.
CGPA: This is an acronym for Cumulative Grade Point Average. It is used to determine a student's class of degree, which depends on the interval a student's point falls in.
Test: When grading test scores like the SAT, for example, the numbers from 0 to 200 are not used when scaling the raw score to the section score. In this case, absolute zero is not used as a reference point. Therefore, it is an interval the score is an interval variable.

Categories of Interval Variable

There are 2 main categories of interval variables, namely; normal distribution and non-normal distributions.

Normal Distribution: It is also called Gaussian distribution and is used to represent real-valued random variables with unknown distribution. This can be further divided into matched and unmatched samples
Non-Normal Distribution: It can also be called the Non-Gaussian distribution, and is used to represent real-valued random variables with known distribution. It can also be further divided into matched and unmatched samples.

Ratio Variable

The ratio variable is one of the 2 types of continuous variables, where the interval variable is the 2nd. It is an extension of the interval variable and is also the peak of the measurement variable types.

The only difference between the ratio variable and interval variable is that the ratio variable already has a zero value. For example, temperature, when measured in Kelvin is an example of ratio variables.

The presence of a zero-point accommodates the measurement in Kelvin. Also, unlike the interval variable multiplication and division operations can be performed on the values of a ratio variable.

Characteristics of Ratio Variable

Ratio variables have absolute zero characteristics. The zero point makes is what makes it possible to measure multiple values and perform multiplication and division operations. Therefore, we can say that an object is twice as big or as long as another.
It has an intrinsic order with an equidistant scale. That is, all the levels in the ratio scale has an equal distance.
Due to the absolute point characteristics of a ratio variable, it doesn't have a negative number like an interval variable. Therefore, before measuring any object on a ratio scale, researchers need to first study if it satisfies all the properties of an interval variable and also the zero point characteristic.
Ratio variable is the peak type of measurement variable in statistical analysis. It allows for the addition, interaction, multiplication, and division of variables.

Also, all statistical analysis including mean, mode, median, etc. can be calculated on the ratio scale.

Examples of Ratio Variable

Here are some examples of ratio variables according to their uses:

Multiple Choice Questions

Multiple choice questions are mostly used for academic testing and ratio variables are sometimes used in this case. Especially for mathematics tests, or word problems we see many examples of ratio variables.

E.g. If Frank is 20 years old and Paul is twice as old as Frank. How old will Paul be in the next 10 years?

20
30
40
50
60
Surveys/Questionnaires

Organizations use this tool whenever they want to get feedback about their product or service, perform market research, and competitive analysis. They use ratio variables to collect relevant data from respondents.

How much time do you spend on the internet daily?

Less than 2 hours
3-4 hours
4-5 hours
5-6 hours
More than 6 hours
Measurement

When registering for National passport, National ID Card, etc. there is always a need to profile applicants. As part of this profiling, a record of the applicant's height, weight, etc. is usually taken.

What is your height in feet and inches?

Less than 5ft
5ft 1inch – 5ft 4Inches
5ft 5Inches – 5ft 9Inches
6ft and above

E.g.2. What is your weight in kgs?

Less than 50 kgs
51- 70 kgs
71- 90 kgs
91-110 kgs
More than 110 kgs

Categories of Ratio Variable

The categories of ratio variables are the same as that of interval variables. Ratio variables are also classified into Gaussian and Non-Gaussian distributions.

They are both further divided into matched and unmatched samples.

Conclusion

The classification of variables according to their measurement type is very useful for researchers in concluding which analytical procedure should be used. It helps to determine the kind of data to be collected, how to collect it and which method of analysis should be used.

For a nominal variable, it is quite easy to collect data through open-ended or closed-ended questions. However, there is also a lot of downsides to this, as nominal data is the simplest data type and as such has limited capabilities.

Ratio variable, on the other hand, is the most complex of the measurement variables and as such can be used to perform the most complex analysis. Even at that, it may be unnecessarily complex times and one of the other variable types will be a better option.

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Source: https://www.formpl.us/blog/nominal-ordinal-interval-ratio-variable-example