Scales of Measurement: Quantifying your variables for unblemished data analysis

Data analysis, regarded as the backbone of research, provides insights into meaningful information/data required to arrive at significant findings. Typically, the data include variables (quantitative or qualitative) such as price, income, performance, knowledge, etc. These data, via measurement & scaling techniques, should be transformed into numerical form to perform further analysis.

Statistics include four major scales of measurement that are utilised to categorise the variables under investigation. The various types of scale of measurement include nominal, ordinal, interval and ratio. 

The measurement process comprises assigning numbers to observations while complying to the rules. The approach through which the numbers are assigned defines the scale of measurement. Each scale of measurement represents a specific property of the number system. These include:

  • Identity – This refers to the assignment of numbers to the response of the research participants. These numbers are used only for the purpose of identification and cannot be employed for mathematical operations. For instance, 1 can be assigned to sample A and 2 to sample B or 1 to sample B and 2 to sample 1 would make no difference in the mathematical operation. The variables with this property are measured on a nominal scale. 
  • Magnitude – Variables, in addition to identification, can magnitude as well. This simply means that the numbers include inherent order from smaller to larger. For example, level of education or position in the class. Here, the variables have a number for identification and also have some order. That is, the variables have 1, 2, and so on as an identification number and an order. This is because the difference in marks between first students maybe 20 and the second & third student maybe 10, meaning that the difference between them is not the same. Variables with both identity and magnitude are measured on an ordinal scale.
  • Absolute zero – True or absolute zero means that the zero as a response demonstrates the absence of the property under measurement. For example, no behaviour, no money, etc. However, the temperature on zero cannot be regarded as absolute zero as it would still have an effect, and we cannot term as there is no temperature.  
  • Equal intervals – This property simply means that the difference between the numbers remains the same throughout the scale. For instance, the difference between 5 and 8 is similar to the difference between 14 and 17. Variables with magnitude, identification and equal intervals properties are measured on an interval scale. 

With that said, knowing the scale of measurement is essential as different statistical tests involve variables with different scale of measurement. For instance, a chi-square test is appropriate for nominal level, whereas Mann-Whitney is apt for ordinal level dependent data. 

Prior to determining which test uses which variable, it is a must to know different types of scale of measurement.

  • Nominal scale of measurement 

This type of measurement is the lowest level that can be used in statistics. It identifies the variables with a unique value under the study. Nominal scale does not assign numerical values to the variable. Instead, categorises data without any definite structure or order. For example, consider colours such as orange, red, and blue. Assign them numbers 1,2, 3 or any other numbers. Here, the purpose of the numbers is used to provide identity to the colours and not to represent descending or ascending order. The only mathematical operation that can be performed here is to count the data. 

  • Ordinal scale of measurement 

Although similar to nominal scale, this type of measurement has advanced features. That is, it has both identity and magnitude. It categorises value assigned to the variables based on their magnitude. Some values may be greater, and some others may be lesser. Such values are arranged in ascending or descending order accordingly, resulting in the ordered relationship between the values. However, the categorised value on the scale need not have fixed intervals. For example, consider the results of a horse race, where the horse that won is placed first, horse close to winning line is placed second and so on. Nevertheless, this scale doesn’t determine if the race was close or the horse won by 2 miles. 

  • Interval scale of measurement

This type of measurement has properties of both nominal and ordinal level. This means that the interval scale of measurement assigns a unique value to each variable under study as well as categorises value in ascending or descending order. The unique property of the measurement scale is that it categorises values in equal intervals. For instance, on the Fahrenheit scale, the difference between 30 & 40 degrees Fahrenheit is equal 50 & 60 degrees Fahrenheit. 

  • Ratio scale of measurement 

This scale of measurement satisfies identity, magnitude, equal intervals and absolute zero properties. Additionally, ratio scale has fixed zero points, and no value exists property, i.e., every value can be measured from starting point or absolute zero. Unlike other measurements, this scale can be used to perform mathematical operations. The best example here is the weight scale. Each value in the scale has a definite meaning, weights can be ordered, and the scale has minimum zero value. 

Scale of measurement is associated with the different mathematical assumption of statistical tests. Therefore, care must be taken while aligning the tests with scale of measurement of variables. 

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