Scales of measurement
One of the most important concepts in statistics is the scale of measurement, which determines how data can be classified, analyzed, and interpreted. Different scales of measurement have different properties and levels of precision, and they also affect the choice of statistical methods and techniques. In this answer, we will explain the four types of scales of measurement: nominal, ordinal, interval, and ratio, and provide examples of each one. We will also discuss the advantages and disadvantages of each scale, and how to choose the appropriate one for your research question.
Nominal scale
Nominal scale is the lowest level of measurement that assigns labels or names to different categories or groups of data. The categories are mutually exclusive and have no inherent order or ranking. For example, gender, blood type, and college major are nominal variables. You can only count the frequency of each category, but you cannot perform any mathematical operations on them.
Ordinal scale
Ordinal scale is the next level of measurement that assigns labels or names to different categories or groups of data, but also allows you to rank them according to some criterion. The categories have a natural order or hierarchy, but the distance between them is not equal or known. For example, ratings, rankings, and preferences are ordinal variables. You can compare the categories and find the median, but you cannot calculate the mean or standard deviation.
Interval scale
Interval scale is the third level of measurement that assigns numerical values to different categories or groups of data, and also allows you to measure the distance between them. The categories have a natural order and a fixed unit of measurement, but the zero point is arbitrary or meaningless. For example, temperature, IQ score, and calendar year are interval variables. You can compare the categories and find the mean and standard deviation, but you cannot calculate ratios or proportions.
Ratio scale
Ratio scale is the highest level of measurement that assigns numerical values to different categories or groups of data, and also allows you to measure the distance and ratio between them. The categories have a natural order, a fixed unit of measurement, and a meaningful zero point that indicates the absence of the attribute. For example, height, weight, and income are ratio variables. You can compare the categories and find the mean, standard deviation, ratio, and proportion
