What is a Measurement Scale?
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.
Characteristics of a Measurement Scale
Identity refers to 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 Female 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 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 means that the scale 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, 2nd position in 20.8 seconds while the 3rd in 30 seconds.
A variable that has an identity, magnitude, and the equal interval is measured on an interval scale.
Absolute zero is a 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.
Levels of Data Measurement
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.