A Variable Measured on an Ordinal Scale is Never Continuous

Levels of Measurement in Statistics

To perform statistical analysis of data, it is important to first understand variables and what should be measured using these variables. There are different levels of measurement in statistics and data measured using them can be broadly classified into qualitative and quantitative data.

First,  let's understand what a variable is.  A quantity whose value changes across the population and can be measured is called variable. For instance, consider a sample of employed individuals. The variables for this set of the population can be industry, location, gender, age, skills, job-type, paid time off, etc The value of the variables will differ with each employee spotlight.

For example, it is practically impossible to calculate the average hourly rate of a worker in the US. So, a sample audience is randomly selected such it represents the larger population appropriately. Then the average hourly rate of this sample audience is calculated. Using statistical tests, you can conclude the average hourly rate of a larger population.

The level of measurement of a variable decides the statistical test type to be used. The mathematical nature of a variable or in other words, how a variable is measured is considered as the level of measurement.

What are Nominal, Ordinal, Interval and Ratio Scales?

Nominal, Ordinal, Interval, and Ratio are defined as the four fundamental levels of measurement scales that are used to capture data in the form of surveys and questionnaires, each being a multiple choice question.

Each scale is an incremental level of measurement, meaning, each scale fulfills the function of the previous scale, and all survey question scales such as Likert, Semantic Differential, Dichotomous, etc, are the derivation of this these 4 fundamental levels of variable measurement. Before we discuss all four levels of measurement scales in details, with examples, let's have a quick brief look at what these scales represent.

Nominal scale is a naming scale, where variables are simply "named" or labeled, with no specific order. Ordinal scale has all its variables in a specific order, beyond just naming them. Interval scale offers labels, order, as well as, a specific interval between each of its variable options.  Ratio scale bears all the characteristics of an interval scale, in addition to that, it can also accommodate the value of "zero" on any of its variables.

Here's more of the four levels of measurement in research and statistics: Nominal, Ordinal, Interval, Ratio.

Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn't involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options.

There are cases where this scale is used for the purpose of classification – the numbers associated with variables of this scale are only tags for categorization or division. Calculations done on these numbers will be futile as they have no quantitative significance.

For a question such as:

Where do you live?

• 1- Suburbs
• 2- City
• 3- Town

Nominal scale is often used in research surveys and questionnaires where only variable labels hold significance.

For instance, a customer survey asking "Which brand of smartphones do you prefer?" Options : "Apple"- 1 , "Samsung"-2, "OnePlus"-3.

• In this survey question , only the names of the brands are significant for the researcher conducting consumer research or netnography. There is no need for any specific order for these brands. However, while capturing nominal data, researchers conduct analysis based on the associated labels.
• In the above example, when a survey respondent selects Apple as their preferred brand, the data entered and associated will be "1". This helped in quantifying and answering the final question – How many respondents selected Apple, how many selected Samsung, and how many went for OnePlus – and which one is the highest.
• This is the fundamental of quantitative research, and nominal scale is the most fundamental research scale.

Nominal Scale Data and Analysis

There are two primary ways in which nominal scale data can be collected:

1. By asking an open-ended question , the answers of which can be coded to a respective number of label decided by the researcher.
2. The other alternative to collect nominal data is to include a multiple choice question in which the answers will be labeled.

In both cases, the analysis of gathered data will happen using percentages or mode,i.e., the most common answer received for the question. It is possible for a single question to have more than one mode as it is possible for two common favorites can exist in a target population.

Nominal Scale Examples

• Gender
• Political preferences
• Place of residence

What is your Gender?	What is your Political preference?	Where do you live?
M- Male F- Female	1- Independent 2- Democrat 3- Republican	1- Suburbs 2- City 3- Town

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Nominal Scale SPSS

In SPSS, you can specify the level of measurement as scale (numeric data on an interval or ratio scale), ordinal, or nominal. Nominal and ordinal data can be either string alphanumeric or numeric.

Upon importing the data for any variable into the SPSS input file, it takes it as a scale variable by default since the data essentially contains numeric values. It is important to change it to either nominal or ordinal or keep it as scale depending on the variable the data represents.

Ordinal Scale: 2^nd Level of Measurement

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as 'Ordinal' sounds similar to 'Order', which is exactly the purpose of this scale.

Ordinal Scale maintains descriptional qualities along with an intrinsic order but is void of an origin of scale and thus, the distance between variables can't be calculated. Descriptional qualities indicate tagging properties similar to the nominal scale, in addition to which, the ordinal scale also has a relative position of variables. Origin of this scale is absent due to which there is no fixed start or "true zero".

Ordinal Data and Analysis

Ordinal scale data can be presented in tabular or graphical formats for a researcher to conduct a convenient analysis of collected data. Also, methods such as Mann-Whitney U test and Kruskal–Wallis H test can also be used to analyze ordinal data. These methods are generally implemented to compare two or more ordinal groups.

In the Mann-Whitney U test, researchers can conclude which variable of one group is bigger or smaller than another variable of a randomly selected group. While in the Kruskal–Wallis H test, researchers can analyze whether two or more ordinal groups have the same median or not.

Learn about: Nominal vs. Ordinal Scale

Ordinal Scale Examples

Status at workplace, tournament team rankings, order of product quality, and order of agreement or satisfaction are some of the most common examples of the ordinal Scale. These scales are generally used in market research to gather and evaluate relative feedback about product satisfaction, changing perceptions with product upgrades, etc.

For example, a semantic differential scale question such as:

How satisfied are you with our services?

• Very Unsatisfied – 1
• Unsatisfied – 2
• Neutral – 3
• Satisfied – 4
• Very Satisfied – 5

1. Here, the order of variables is of prime importance and so is the labeling. Very unsatisfied will always be worse than unsatisfied and satisfied will be worse than very satisfied.
2. This is where ordinal scale is a step above nominal scale – the order is relevant to the results and so is their naming.
3. Analyzing results based on the order along with the name becomes a convenient process for the researcher.
4. If they intend to obtain more information than what they would collect using a nominal scale, they can use the ordinal scale.

This scale not only assigns values to the variables but also measures the rank or order of the variables, such as:

• Grades
• Satisfaction
• Happiness

How satisfied are you with our services?

• 1- Very Unsatisfied
• 2- Unsatisfied
• 3- Neural
• 4- Satisfied
• 5- Very Satisfied

Interval Scale: 3^rd Level of Measurement

Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables. Variables that have familiar, constant, and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale too, 'Interval' indicates 'distance between two entities', which is what Interval scale helps in achieving.

These scales are effective as they open doors for the statistical analysis of provided data. Mean, median, or mode can be used to calculate the central tendency in this scale. The only drawback of this scale is that there no pre-decided starting point or a true zero value.

Interval scale contains all the properties of the ordinal scale, in addition to which, it offers a calculation of the difference between variables. The main characteristic of this scale is the equidistant difference between objects.

For instance, consider a Celsius/Fahrenheit temperature scale –

• 80 degrees is always higher than 50 degrees and the difference between these two temperatures is the same as the difference between 70 degrees and 40 degrees.
• Also, the value of 0 is arbitrary because negative values of temperature do exist – which makes the Celsius/Fahrenheit temperature scale a classic example of an interval scale.
• Interval scale is often chosen in research cases where the difference between variables is a mandate – which can't be achieved using a nominal or ordinal scale. The Interval scale quantifies the difference between two variables whereas the other two scales are solely capable of associating qualitative values with variables.
• The mean and median values in an ordinal scale can be evaluated, unlike the previous two scales.
• In statistics, interval scale is frequently used as a numerical value can not only be assigned to variables but calculation on the basis of those values can also be carried out.

Even if interval scales are amazing, they do not calculate the "true zero" value which is why the next scale comes into the picture.

Interval Data and Analysis

All the techniques applicable to nominal and ordinal data analysis are applicable to Interval Data as well. Apart from those techniques, there are a few analysis methods such as descriptive statistics, correlation regression analysis which is extensively for analyzing interval data.

Descriptive statistics is the term given to the analysis of numerical data which helps to describe, depict, or summarize data in a meaningful manner and it helps in calculation of mean, median, and mode.

Interval Scale Examples

• There are situations where attitude scales are considered to be interval scales.
• Apart from the temperature scale, time is also a very common example of an interval scale as the values are already established, constant, and measurable.
• Calendar years and time also fall under this category of measurement scales.
• Likert scale , Net Promoter Score , Semantic Differential Scale , Bipolar Matrix Table, etc. are the most-used interval scale examples.

The following questions fall under the Interval Scale category:

• What is your family income?
• What is the temperature in your city?

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Ratio Scale: 4^th Level of Measurement

Ratio Scale is defined as a variable measurement scale that not only produces the order of variables but also makes the difference between variables known along with information on the value of true zero. It is calculated by assuming that the variables have an option for zero, the difference between the two variables is the same and there is a specific order between the options.

With the option of true zero, varied inferential, and descriptive analysis techniques can be applied to the variables. In addition to the fact that the ratio scale does everything that a nominal, ordinal, and interval scale can do, it can also establish the value of absolute zero. 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.

• Ratio scale provides the most detailed information as researchers and statisticians can calculate the central tendency using statistical techniques such as mean, median, mode, and methods such as geometric mean, the coefficient of variation, or harmonic mean can also be used on this scale.
• Ratio scale accommodates the characteristic of three other variable measurement scales, i.e. labeling the variables, the significance of the order of variables, and a calculable difference between variables (which are usually equidistant).
• Because of the existence of true zero value, the ratio scale doesn't have negative values.
• To decide when to use a ratio scale, the researcher must observe whether the variables have all the characteristics of an interval scale along with the presence of the absolute zero value.
• Mean, mode and median can be calculated using the ratio scale.

Ratio Data and Analysis

At a fundamental level, Ratio scale data is quantitative in nature due to which all quantitative analysis techniques such as SWOT, TURF, Cross-tabulation, Conjoint, etc. can be used to calculate ratio data. While some techniques such as SWOT and TURF will analyze ratio data in such as manner that researchers can create roadmaps of how to improve products or services and Cross-tabulation will be useful in understanding whether new features will be helpful to the target market or not.

Ratio Scale Examples

The following questions fall under the Ratio Scale category:

• What is your daughter's current height?
  • Less than 5 feet.
  • 5 feet 1 inch – 5 feet 5 inches
  • 5 feet 6 inches- 6 feet
  • More than 6 feet
• What is your weight in kilograms?
  • Less than 50 kilograms
  • 51- 70 kilograms
  • 71- 90 kilograms
  • 91-110 kilograms
  • More than 110 kilograms

Learn about: Interval vs. Ratio Scale

Summary –  Levels of Measurement

The four data measurement scales – nominal, ordinal, interval, and ratio –  are quite often discussed in academic teaching. Below easy-to-remember chart might help you in your statistics test.

Offers:	Nominal	Ordinal	Interval	Ratio
The sequence of variables is established	–	Yes	Yes	Yes
Mode	Yes	Yes	Yes	Yes
Median	–	Yes	Yes	Yes
Mean	–	–	Yes	Yes
Difference between variables can be evaluated	–	–	Yes	Yes
Addition and Subtraction of variables	–	–	Yes	Yes
Multiplication and Division of variables	–	–	–	Yes
Absolute zero	–	–	–	Yes

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Source: https://www.questionpro.com/blog/nominal-ordinal-interval-ratio/

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