SCALE & MEASUREMENT

Measurement and Scale in Research Methodology. Measurement is the process of describing some property of a phenomenon under study and assigning a numerical value to it. Measurement is considered as the foundation of scientific inquiry. In our daily life, many things are measured continuously in different ways for different purposes. 

We can not only measure physical objects but abstract objects also, that means we can measure quantitatively and qualitatively. We can measure height, weight, length, width, income etc., (quantitative measurement) and at the same time, we can measure attitude, personality, perception, intelligence, preference (qualitative measurement) etc. A measurement can give us different kinds of information about a theoretical concept under study. 

A more contemporary definition of measurement as “the estimation or the discovery of the ratio of some magnitude of a quantitative attribute to a unit of the same attribute” (Michell, 1997).

According to Warren S Torgerson “The assignment of numbers to objects to represent amounts or degrees of a property possessed by all of the objects.” To understand the nature of the data, we must know at which level the data is measured. So the measurement can occur at different levels, and the relationship among the values assigned determines the level of measurement. There are four hierarchical levels of measurement identified by Stevens (1946); they are nominal, ordinal, interval, and ratio.

Nominal Scale

This is a method of measuring the objects or events into a discrete category.   This is regarded as the most basic form of measurement.  Here we assign a number to an object only for the identification of the object.   So it is a categorical data or qualitative data.  Here the numbers are only used for labeling the object, and there is no quantitative value at all.  This is used to categories the data into different groups.  In a survey, all the respondence are divided into different categories, which should be mutually exclusive and collectively exhaustive. Here the categories have no predefined order. 

Examples of nominal scale data connection using a questionnaire.

1. Specify your gender
   1. Male
   2. Female
2. Are you Married?
   1. Yes
   2. No
3. You are from
   1. Urban
   2. Rural
4. Specify your working department
   1. Marketing
   2. HR
   3. Finance
   4. Sales
   5. Production
   6. Operations
5. Specify your food habit
   1. Vegetarian
   2. No-Vegetarian

Here we can assign number to each option like 1 to Male and 2 to female, and 1 to Yes, and 2 to No, 1 to Urban, 2 to Rural, 1 to Marketing, 2 to HR, 3 to Finance etc.

Here these numbers have no quantitative values; they only represent the category.  So we cannot apply any arithmetic operations in this type of sale.  We can only count the number of items in each category.

Here we can prepare a frequency distribution table for representing this nominal data.

Ordinal Scale

The ordinal scale is the next level of data measurement scale.  Here we measure according to the rank order of the data without considering the degree of difference between the data.  Here the “Ordinal” is the indication of “Order”.  In ordinal measurement, we assign a numerical value to the variables based on their relative ranking or positioning in comparison with other data in that group. An ordinal scale is indicating the logical hierarchy among variables under observation.

Here the data has an order.  In a nominal scale, there is no predefined order for arranging the data.  But here the data is arranged according to some predefined order, but not considering the magnitude of difference.  The ranking scale tells us the relative position of the objects under study.

Suppose in a 100-meter race John finished first, Tom finished second, Mathew finished 3 and Xavier finished fourth.  Here we explain the data in ranking scale.  We arrange the data according to the relative position of the data set.  Here we not consider the magnitude of difference between John and Tom, Tom and Mathew, Mathew and Xavier.  They may not finish in the equal interval, that is Tom finished 5 seconds after John, Mathew finished 9 seconds after Tom, and Xavier finished 18 seconds after Mathew.  Here we do not consider this magnitude of difference, but only the order of the finishing position.

Examples of Ordinal scale data (Rank Scale) connection using a questionnaire.

Example: Rank your feature preferences when you buy a mobile phone. The most preferred feature should be ranked one, the second preferred feature should be rank two and so on.

Rank the following mobile brand in order of your preference, the most preferred mobile brand should be ranked one, the second most preferred should be ranked two and so on.

To know the descriptive analysis of the ranking scale, watch the video.

Ranking Scale Questionnaire - How to tabulate, analyse and prepare graph using MS Excel.

Watch this video on YouTube.

Interval Scale

It is the next higher level of measurement. It overcomes the limitation of ordinal scale measurement. In the ordinal scale, the magnitude of the difference is unimportant, but here on an interval scale, the magnitude of the difference is important. In the interval scale, the difference between the two variables has a meaningful interpretation. In the interval scale, the difference between variables is equal distance. The distance between any two adjacent attributes is called an interval, and intervals are always equal.

Examples of Interval Scale data connection using questionnaire.

How likely do you recommend our product to your friends or relatives?

Likert scale is a tool to collect interval data, which is developed by Rensis Likert

To know the descriptive analysis of the interval scale , watch the video.

How to tabulate, analyze, and prepare graph from Likert Scale questionnaire data using Ms Excel.

Watch this video on YouTube.

Ratio Scale

Ratio scale is purely quantitative.  Among the four levels of measurement, ratio scale is the most precise.  The score of zero in ratio scale is not arbitrary compared to the other three scales.

This is the unique quality of ratio scale data.  It represents all the characteristics of nominal, ordinal, and interval scales.  Examples of ratio scales are age, wight, height, income, distance etc.

Examples of Interval Scale (Ranking Scale) data connection using questionnaire.

Specify you monthly income :

How many students are there in your institution? :

Number of departments in your organisation :