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.
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.
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.
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.
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.
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.
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.
How do you think we can improve our service?
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.
How long have you been using our product?
There are 2 main categories of nominal variables, namely; the matched and unmatched categories.
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.
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.
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.
How satisfied are you with our service tonight?
How satisfied are you with our service tonight?
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?
Interval Scale: each response in an interval scale is an interval on its own.
How old are you?
There are also 2 main categories of ordinal variables, namely; the matched and unmatched category.
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.
There are 2 main categories of interval variables, namely; normal distribution and non-normal distributions.
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.
Also, all statistical analysis including mean, mode, median, etc. can be calculated on the ratio scale.
Here are some examples of ratio variables according to their uses:
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?
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?
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?
E.g.2. What is your weight in kgs?
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.
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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