## Levels of Measurement in Statistics

Before performing statistical analysis of data it is necessary to first understand variables and what should be measured using these variables. In statistics, there are various types of measurement scales like nominal, ordinal, interval, ratio, and the data collected using them can be divided into qualitative and quantitative categories. Nominal and Ordinal data can be categorized as Qualitative categories. On the other hand, Interval & Ratio are marked as Quantitative categories. We will learn all the Levels of Measurement in Statistics or research methodology.

Let’s start by defining what is variable in research and its types. Variable refers to a quantity whose value varies throughout a population and may be measured. Consider a group of people that are currently employed. Industry, location, gender, age, skills, job type, and so on can be variables for this group of people. Each employee’s value for the variables will be different.

Calculating the average hourly pay of a worker in the United States, for example, is nearly impossible. As a result, a random sample audience is chosen to accurately represent the greater population. After that, the sample audience’s average hourly rate is computed. You can get the average hourly rate of a bigger population using statistical testing.

The statistical test type to be utilized is determined by the level of measurement of a variable. The degree of measurement refers to a variable’s mathematical nature, or, in other words, how it is measured.

## What are the differences between Nominal, Ordinal, Interval, and Ratio Scales?

The four primary types of measurement scales that are used to record data in the form of surveys and questionnaires, each being a multiple-choice question, are characterized as Nominal, Ordinal, Interval, and Ratio.

All survey question scales, such as Likert, Semantic Differential, Dichotomous, and others, are derived from these four fundamental levels of variable assessment. Let’s take a short look at what these scales represent before we go over all four levels of measuring scales in detail with examples.

A nominal scale is a naming scale in which variables are simply “named” or “labeled,” with no particular order in mind. Beyond only naming the variables, the ordinal scale has them in a predefined sequence. Labels, order, and a precise interval between each of the variable possibilities are all available on the interval scale. In addition to having all of the qualities of an interval scale, a ratio scale can also accommodate the value of “zero” on any of its variables.

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In research and statistics, there are four levels of measurement: nominal, ordinal, interval, and ratio. Let’s discuss it with examples.

## Nominal: First Levels of Measurement in Statistics

The nominal scale, also known as the categorical variable scale, is a scale that does not contain a numerical value or order and is used to categorize variables into separate classifications. The easiest of the four variable measurement scales is this one. Calculations on these variables will be fruitless because the options have no numerical value.

In certain circumstances, this scale is used for classification — the numbers linked with the scale’s variables are just labels for categorization or division. Calculations based on these figures are pointless because they lack quantitative relevance.

**If you’re asked a question like this, can be categorized as a nominal variable:**

What city do you call home?

1. Suburbs

2. City

3. Town

In research surveys and questionnaires, the nominal scale is frequently employed when just the variable labels are significant.

For example, a customer survey can inquire,

“**Which smartphone brand do you prefer?**”

“Apple” is number one,

“Samsung” is number two, and

“OnePlus” is number three.

Only the brand names matter in this survey question for the consumer research researcher. For these brands, there is no need to place a separate order. Researchers, on the other hand, undertake an analysis based on the linked labels while collecting nominal data.

When a survey respondent selects Apple as their preferred brand in the example above, the data entered and related will be “1.” This helped quantify and answer the last question – how many people chose Apple, how many chose Samsung, and how many chose OnePlus – and which option was the most popular.

The most basic research scale is the nominal scale, which is the foundation of quantitative research.

### Data and Analysis on a Nominal Scale

There are two basic methods for collecting nominal scale data:

By posing an open-ended inquiry, the respondent’s responses can be tagged to a specific label number determined by the researcher. Another option for collecting nominal data is to include a multiple-choice question with labeled responses.

In all circumstances, the acquired data will be analyzed using percentages or mode, which is the most common response to the query. It is possible for a single question to have more than one mode, just as it is possible for a target demographic to have two common favorites.

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## Ordinal: Second Levels of Measurement in Statistics

Ordinal Scale is a type of variable measurement scale that is used to show the order of variables rather than the differences between them. These scales are commonly used to represent non-mathematical concepts like frequency, pleasure, happiness, pain level, and so on. The implementation of this scale is simple to remember because the word “Ordinal” sounds close to the word “Order,” which is exactly what this scale is for. That means it deals with the ranking of any categorical variables.

Ordinal Scale takes descriptional features as well as intrinsic order, but lacks an origin of scale, making it impossible to compute the distance between variables. The ordinal scale has a relative position of variables, which is analogous to the nominal scale. Descriptional attributes imply tagging properties similar to the nominal scale. Because there is no definite start or “true zero” on this scale, there is no fixed start or “true zero.”

### Data and Analysis of Ordinal Values

For a researcher to conduct a convenient analysis of obtained data, ordinal scale data can be provided in tabular or graphical representations. Ordinal data can also be analyzed using methods like the Mann-Whitney U test and the Kruskal–Wallis H test. In most cases, these approaches are used to compare two or more ordinal groupings.

Researchers can use the Mann-Whitney U test to determine whether a variable in one group is larger or smaller than a variable in a randomly selected group. Researchers can use the Kruskal–Wallis H test to see if two or more ordinal groups have the same median or not.

**Examples of Ordinal Scale:**The ordinal scale is used to rank workplace status, tournament team ranks, product quality order, and order of agreement or satisfaction, among other things. These scales are commonly used in market research to collect and evaluate relative feedback on product satisfaction, changing views as a result of product improvements, and so on. Consider the following semantic differential scale question:

What level of satisfaction do you have with our services?

1 Unsatisfied

2 Neutral

3 Satisfied

4 Very Unsatisfied

5 Extremely Satisfied

The order of the variables, as well as the labeling, are critical here. Very dissatisfied is always worse than dissatisfied, and satisfied is always worse than satisfied. This is where the ordinal scale differs from the nominal scale in that the order of the outcomes, as well as their name, is important.

For the researcher, analyzing results based on the order and name becomes a simple task.

They can utilize the ordinal scale if they want to capture more information than they could use a nominal scale.

This scale not only assigns values to variables but also determines their rank or order, such as Grades \ Satisfaction \ Happiness.

What level of satisfaction do you have with our services?

1- Very Unsatisfied

2- Unsatisfied

3- Neural

4- Satisfied

5- Very Satisfied

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## Interval: Third Levels of Measurement in Statistics

The term “interval scale” refers to a numerical scale in which the order of the variables as well as the difference between them are known. The Interval scale is used to classify variables that have predictable, consistent, and calculable differences. It’s also simple to recall the scale’s fundamental function: the word “interval” means “distance between two entities,” which is exactly what the Interval scale aids in attaining.

These scales are successful because they allow for statistical analysis of the data presented. The central tendency of this scale can be calculated using the mean, median, or mode. The only disadvantage of this scale is the lack of a predetermined starting point or a true zero value.

The interval scale has all of the qualities of the ordinal scale plus the ability to calculate the difference between variables. The equidistant distance between items is the scale’s most distinguishing feature.

**Consider a temperature scale in Celsius and Fahrenheit —**

- The difference between these two temperatures is the same as the difference between 70 and 40 degrees. 80 degrees is always greater than 50 degrees.
- Also, because negative temperatures exist, the value of 0 is arbitrary, making the Celsius/Fahrenheit temperature scale a classic example of an interval scale.
- When the difference between variables is a requirement – which cannot be met using a nominal or ordinal scale – the interval scale is frequently used. The Interval scale measures the difference between two variables, whereas the other two scales can only assign qualitative values to variables.
- Unlike the previous two scales, the mean and median values of an ordinal scale can be examined.
- In statistics, the interval scale is commonly employed because a numerical value may be assigned to variables as well as calculations based on those values.

Even while interval scales are fantastic, they do not calculate the “real zero” value, which is why the next scale is needed.

### Data Analysis of Interval Scale

All of the approaches used to analyze nominal and ordinal data apply to interval data as well. Apart from those techniques, there are a few analysis methods for examining interval data, such as descriptive statistics and correlation regression analysis.

Descriptive statistics is the name given to a type of statistical analysis that helps to explain, depict, or summarize numerical data in an understandable way, as well as calculate mean, median, and mode.

**Examples of Interval Scales:**

- Attitude scales can be considered interval scales in some cases.
- Time, like the temperature scale, is a typical example of an interval scale because the values are previously known, constant, and measured.
- This category of measurement scales also includes calendar years and time.
- The most common interval scales include the Likert scale, Net Promoter Score, Semantic Differential Scale, Bipolar Matrix Table, and others.

**The Interval Scale category includes the following questions:**How much money does your family make?

What’s the weather like in your town?

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## Ratio: Fourth Levels of Measurement in Statistics

A ratio scale is a variable measurement scale that not only determines the order of variables but also the difference between them, as well as information on the true zero value. It is calculated by assuming that each variable has a zero option, that the difference between the two variables is the same, and that the alternatives are in a specified order.

Variables can be analyzed using various inferential and descriptive analysis techniques with true zero as an option. In addition to performing all of the functions of a nominal, ordinal, and interval scale, the ratio scale may additionally determine the value of absolute zero. Weight and height are two of the most common ratio scales. A ratio scale is used in market research to measure market share, annual sales, the price of a new product, the number of consumers, and so on.

- Researchers and statisticians can compute the central tendency using statistical techniques such as mean, median, mode, and approaches such as geometric mean, coefficient of variation, or harmonic mean on the ratio scale, which provides the most thorough information.
- The characteristics of three additional variable measurement scales, namely identifying the variables, the significance of the order of variables, and a calculable difference between variables, are all accommodated by the ratio scale (which are usually equidistant).
- The ratio scale does not have negative values because there is an actual zero value.
- When deciding whether or not to utilize a ratio scale, the researcher must look for all of the properties of an interval scale, as well as the presence of the absolute zero value.
- The ratio scale can be used to calculate the mean, mode, and median.

### Data and Analysis on Ratios

Due to the fact that ratio scale data is quantitative in nature, it may be calculated using any quantitative analytic tool such as SWOT, TURF, Cross-tabulation, Conjoint, and so on. While certain techniques, such as SWOT and TURF, can evaluate ratio data in such a way that researchers may construct roadmaps for how to improve products or services, Cross-tabulation will be effective in determining whether or not new features will be beneficial to the target market.

**Examples of Ratio Scales:**The Ratio Scale category includes the following questions:

**What is the current height of your daughter?**-Less than 5 feet.

-5 feet 1 inch – 5 feet 5 inches

-5 feet 6 inches- 6 feet

-More than 6 feet

**How many kilograms do you weigh?**-50 kilos or less

-51 to 70 kg

-weighing between 71 and 90 kilos

-91 to 110 kg

-Approximately 110 kilos

## Summary: Levels of Measurement At a Glance

In academic teaching, the four data measurement scales — nominal, ordinal, interval, and ratio – are frequently discussed. The easy-to-remember chart below may assist you in passing your statistics test.

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