Scales of measurement in research and statistics are the different ways in which variables are defined and grouped into different categories. Sometimes called the level of measurement, it describes the nature of the values assigned to the variables in a data set.

The term scale of measurement is derived from two keywords in statistics, namely; measurement and scale. Measurement is the process of recording observations collected as part of the research.

Scaling, on the other hand, is the assignment of objects to numbers or semantics. These two words merged together refer to the relationship among the assigned objects and the recorded observations.

A measurement scale is used to qualify or quantify data variables in statistics. It determines the kind of techniques to be used for statistical analysis.

There are different kinds of measurement scales, and the type of data being collected determines the kind of measurement scale to be used for statistical measurement. These measurement scales are four in number, namely; nominal scale, ordinal scale, interval scale, and ratio scale.

The measurement scales are used to measure qualitative and quantitative data. With nominal and ordinal scale being used to measure qualitative data while interval and ratio scales are used to measure quantitative data.

Identity is defined as the assignment of numbers to the values of each variable in a data set. Consider a questionnaire that asks for a respondent's gender with the options Male and Female for instance. The values 1 and 2 can be assigned to Male and Females respectively.

Arithmetic operations can not be performed on these values because they are just for identification purposes. This is a characteristic of a nominal scale.

The magnitude is defined as the size of a measurement scale, where numbers (the identity) have an inherent order from least to highest. They are usually represented on the scale in ascending or descending order. The position in a race, for example, is arranged from the 1st, 2nd, 3rd to the least.

This example is measured on an ordinal scale because it has both identity and magnitude.

Equal Intervals are defined as the scale that has a standardized order. I.e., the difference between each level on the scale is the same. This is not the case for the ordinal scale example highlighted above.

Each position does not have an equal interval difference. In a race, the 1st position may complete the race in 20 secs, the 2nd position in 20.8 seconds while the 3rd in 30 seconds.

A variable that has an identity, magnitude, and equal interval is measured on an interval scale.

Absolute zero is defined as the feature that is unique to a ratio scale. It means that there is an existence of zero on the scale, and is defined by the absence of the variable being measured (e.g. no qualification, no money, does not identify as any gender, etc.

The level of measurement of a given data set is determined by the relationship between the values assigned to the attributes of a data variable. For example, the relationship between the values (1 and 2) assigned to the attributes (male and female) of the variable (Gender) is "identity". This via. a nominal scale example.

By knowing the different levels of data measurement, researchers are able to choose the best method for statistical analysis. The different levels of data measurement are: nominal, ordinal, interval, and ratio scales

The nominal scale is a scale of measurement that is used for identification purposes. It is the coldest and weakest level of data measurement among the four.

Sometimes known as categorical scale, it assigns numbers to attributes for easy identity. These numbers are however not qualitative in nature and only act as labels.

The only statistical analysis that can be performed on a nominal scale is the percentage or frequency count. It can be analyzed graphically using a bar chart and pie chart.

**Nominal Scale Example**

In the example below, the measurement of the popularity of a political party is measured on a nominal scale.

Which political party are you affiliated with?

- Independent
- Republican
- Democrat

Labeling Independent as "1", Republican as "2" and Democrat as "3" does not in any way mean any of the attributes are better than the other. They are just used as an identity for easy data analysis.

Ordinal Scale involves the ranking or ordering of the attributes depending on the variable being scaled. The items in this scale are classified according to the degree of occurrence of the variable in question.

The attributes on an ordinal scale are usually arranged in ascending or descending order. It measures the degree of occurrence of the variable.

Ordinal scale can be used in market research, advertising, and customer satisfaction surveys. It uses qualifiers like very, highly, more, less, etc. to depict a degree.

We can perform statistical analysis like median and mode using the ordinal scale, but not mean. However, there are other statistical alternatives to mean that can be measured using the ordinal scale.

**Ordinal Scale Example**

For example: A software company may need to ask its users:

How would you rate our app?

- Excellent
- Very Good
- Good
- Bad
- Poor

The attributes in this example are listed in descending order.

The interval scale of data measurement is a scale in which the levels are ordered and each numerically equal distances on the scale have equal interval difference. If it is an extension of the ordinal scale, with the main difference being the existence of equal intervals.

With an interval scale, you not only know that a given attribute A is bigger than another attribute B, but also the extent at which A is larger than B. Also, unlike ordinal and nominal scale, arithmetic operations can be performed on an interval scale.

**A 5 Minutes Interval Time Scale**

It is used in various sectors like in education, medicine, engineering, etc. Some of these uses include calculating a student's CGPA, measuring a patient's temperature, etc.

**Interval Scale Example**

A common example is measuring temperature on the Fahrenheit scale. It can be used in calculating mean, median, mode, range, and standard deviation.

Ratio Scale is the peak level of data measurement. It is an extension of the interval scale, therefore satisfying the four characteristics of the measurement scale; identity, magnitude, equal interval, and the absolute zero property.

This level of data measurement allows the researcher to compare both the differences and the relative magnitude of numbers. Some examples of ratio scales include length, weight, time, etc.

With respect to market research, the common ratio scale examples are price, number of customers, competitors, etc. It is extensively used in marketing, advertising, and business sales.

The ratio scale of data measurement is compatible with all statistical analysis methods like the measures of central tendency (mean, median, mode, etc.) and measures of dispersion (range, standard deviation, etc.).

**Ratio Scale Example**

For example: A survey that collects the weights of the respondents.

Which of the following category do you fall in? Weigh

- more than 100 kgs
- 81 - 100 kgs
- 61 - 80 kgs
- 40 - 60 kgs
- Less than 40 kgs

Formplus is the best tool for collecting nominal, ordinal, interval and ratio data. It is an easy to use form builder that allows you to collect data with ease. Follow the following steps to collect data on Formplus

We will be using the radio choice multiple-choice questions to collect data on Formplus form builder.

- Sign up or log in to your account on https://www.formpl.us/
- Click the "Choice Options" tab in the form builder menu.
- Click on the Radio button.

- Click on the edit button to edit the form.
- Edit the question and choice options.
- Click the save button to save edits.

- Repeat
**Step 1**. - Click on the edit button to edit the form.
- Edit the question and choice options
- Assign values to the choice options.
- Click the save button to save edits.

- Click on the "+" sign at the bottom to add a new page.

- Repeat
**Step 1**. - Click on the edit button to edit the form.
- Edit the question and choice options.
- Click the save button to save edits.

**Note**: The interval data options do not have a zero value.

- Repeat
**Step 1**. - Click on the edit button to edit the form.
- Edit the question and choice options.
- Click the save button to save edits.
- Click the save button in the top right corner to save the form.

**Note: **that the ratio data example has a zero value, which differentiates it from the interval scale.

There are two main types of measurement scales, namely; comparative scales and non-comparative scales.

In comparative scaling, respondents are asked to make a comparison between one object and the other. When used in market research, customers are asked to evaluate one product in direct comparison to the others. Comparative scales can be further divided into pair comparison, rank order, constant sum, and q-sort scales.

**Paired Comparison Scale**

Paired Comparison scale is a scaling technique that presents the respondents with two objects at a time and asks them to choose one according to a predefined criterion. Product researchers use it in comparative product research by asking customers to choose the most preferred to them in between two closely related products.

**For example,** there are 3 new features in the last release of a software product. But the company is planning to remove 1 of these features in the new release. Therefore, the product researchers are performing a comparative analysis of the most and least preferred feature.

- Which feature is most preferred to you between the following pairs?

- Filter - Voice recorder
- Filter - Video recorder
- Voice recorder - Video recorder
**Rank Order Scale:**

In rank order scaling technique, respondents are simultaneously provided with multiple options and asked to rank them in order of priority based on a predefined criterion. It is mostly used in marketing to measure preference for a brand, product, or feature.

When used in competitive analysis, the respondent may be asked to rank a group of brands in terms of personal preference, product quality, customer service, etc. The results of this data collection are usually obtained in the conjoint analysis, as it forces customers to discriminate among options.

The rank order scale is a type of ordinal scale because it orders the attributes from the most preferred to the least preferred but does not have a specific distance between the attributes.

For example:

Rank the following brands from the most preferred to the least preferred.

- Coca-Cola
- Pepsi Cola
- Dr pepper
- Mountain Dew
**Constant Sum Scale**

Constant Sum scale is a type of measurement scale where the respondents are asked to allocate a constant sum of units such as points, dollars, chips or chits among the stimulus objects according to some specified criterion. The constant sum scale assigns a fixed number of units to each attribute, reflecting the importance a respondent attaches to it.

This type of measurement scale can be used to determine what influences a customer's decision when choosing which product to buy. For example, you may wish to determine how important price, size, fragrance, and packaging is to a customer when choosing which brand of perfume to buy.

Some of the major setbacks of this technique are that respondents may be confused and end up allocating more or fewer points than those specified. The researchers are left to deal with a group of data that is not uniform and may be difficult to analyze.

Avoid this with the logic feature on Formplus. This feature allows you to add a restriction that prevents the respondent from adding more or fewer points than specified to your form.

**Q-Sort Scale**

Q-Sort scale is a type of measurement scale that uses a rank order scaling technique to sort similar objects with respect to some criterion. The respondents sort the number of statements or attitudes into piles, usually of 11.

The Q-Sort Scaling helps in assigning ranks to different objects within the same group, and the differences among the groups (piles) are clearly visible. It is a fast way of facilitating discrimination among a relatively large set of attributes.

For example, a new restaurant that is just preparing its menu may want to collect some information about what potential customers like:

The document provided contains a list of 50 meals. Please choose 10 meals you like, 30 meals you are neutral about (neither like nor dislike) and 10 meals you dislike.

In non-comparative scaling, customers are asked to only evaluate a single object. This evaluation is totally independent of the other objects under investigation. Sometimes called monadic or metric scale, Non-Comparative scale can be further divided into continuous and the itemized rating scales

**Continuous Rating Scale**

In continuous rating scale, respondents are asked to rate the objects by placing a mark appropriately on a line running from one extreme of the criterion to the other variable criterion. Also called the graphic rating scale, it gives the respondent the freedom to place the mark anywhere based on personal preference.

Once the ratings are obtained, the researcher splits up the line into several categories and then assign the scores depending on the category in which the ratings fall. This rating can be visualized in both horizontal and vertical form.

Although easy to construct, the continuous rating scale has some major setbacks, giving it limited usage in market research.

**Itemized Rating Scale**

The itemized rating scale is a type of ordinal scale that assigns numbers each attribute. Respondents are usually asked to select an attribute that best describes their feelings regarding a predefined criterion.

Itemized rating scale is further divided into 2, namely; Likert scale, Stapel scale, and semantic scale.

**Likert Scale**

** **A Likert scale is an ordinal scale with five response categories, which is used to order a list of attributes from the best to the least. This scale uses adverbs of degree like very strongly, highly, etc. to indicate the different levels.

**Stapel Scale:**

This a scale with 10 categories, usually ranging from -5 to 5 with no zero point. It is a vertical scale with 3 columns, where the attributes are placed in the middle and the least (-5) and highest (5) is in the 1st and 3rd columns respectively.

**Semantic Differential Scale**

This is a seven-point rating scale with endpoints associated with bipolar labels (e.g. good or bad, happy, etc.). It can be used for marketing, advertising and in different stages of product development.

If there is more than one item being inherently investigated, it can be visualized on a table with more than 3 columns.

In a nutshell, scales of measurement refers to the various measures used in quantifying the variables researchers use In performing data analysis. They are an important aspect of research and statistics because the level of data measurement is what determines the data analysis technique to be used.

Understanding the concept of scales of measurements is a prerequisite to working with data and performing statistical analysis. The different measurement scales have some similar properties and are therefore important to properly analyze the data to determine its measurement scale before choosing a technique to use for analysis.

A number of scaling techniques are available for the measurement of the same measurement scale. Therefore, there is no unique way of selecting a scaling technique for research purposes.

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