# Scales of Measurement

The following are the four common data measurement levels used:
• Nominal Scale
• Ordinal Scale
• Interval Scale
• Ratio Scale

Nominal Scale – When data labels or names used to identify the attribute of an element, then the nominal scale is used.
For example, assume that a marketing research company wants to conduct a survey in three towns of India – Bhopal, Nagpur and Baroda. While compiling data, the company assigns the numeric code “1” to Bhopal, “2” to Nagpur, and “3” to Baroda. In this case, “1”,”2”,”3” are the labels used to identify the three different towns. Data shows the numeric value but the scale of measurement is nominal. In other words, we cannot say that “1” indicates any ranking or rating; this is only for the sake of convenience in Identification.

Ordinal Scale – In addition to nominal level data capacities, ordinal scale can be used to rank or order objects.
For Example, a manufacturing company administers a questionnaire to 150 consumers for obtaining the consumer perception for one of its products. Each consumer is asked to judge between 3 given options: excellent, good, or poor. Clearly, excellent is ranked the best and poor the worst with good ranked in between the 2. If we want to assign numeric values to these 3 attribute, “1” can be used for excellent, “2” for good, & “3” for poor. In most cases, when we apply statistical tools and techniques, for the sake of interpretation convenience, rankings are set in reverse. In this case, “1” will be used for poor, “2” for good, and “3” for excellent. Therefore, the lowest number has the lowest ranking, & the highest number has the highest ranking. While using this kind of ordinal measurement, the company cannot say that the interval between the ranking points 1 & 2 is equal to the interval between ranking points 2 & 3. Here, it can be stated that 1 is superior followed by 2 & 3, or as in the 2nd case 1, the lowest number, has got the lowest ranking followed by the next 2 numbers, 2 and 3, as the ranking reference for good and excellent. The exact difference between these numeric values cannot be measured in any of these cases. Nominal and Ordinal level data measurements are often used for imprecise measurements such as demographic questions, ranking of items under the study, & the like. This is why these data are termed as non-metric data & are referred to as qualitative data.

Interval Scale – the difference between 2 consecutive numbers is meaningful. Interval data is always numeric.
For Example, 3 students have scored 65, 75 & 85. These 3 students can be rated in terms of their performances. However, the difference in the numbers is also meaningful.
In the interval level of performance, meaningful difference between 2 ranking points can be obtained.

Ratio Scale – Measurements possess all the properties of interval data with meaningful ration to 2 values.
For Example, a company markets 2 toothbrushes prices 30 & 15. In the ration scale the difference between the 2 points is 15, can be calculated and is meaningful. With it, we can also say that the price of 1st product is twice the price of the 2nd product.
Interval and ratio level data are collected using some precise instruments. These data are called metric data & are sometimes referred to as quantitative data.

Section B_Group 5_Kranthi Kiran Gude_12PGP076