Through acts of measurement, observations are either assigned to different categories or quantified using numerical values.
The complete set of categories or values that are used to differentiate between observations is called the scale of measurement. There are a total of four different scales to consider:
These four scales of measurement can be organized hierarchically according to the strength of the data they produce. Data gathered using a nominal scale is considered the weakest, whereas data resulting from a ratio measurement is considered the strongest.
Nominal and ordinal scales use labels to classify observations into different categories and the data resulting from these types of measurement is qualitative in nature. Consequently, no numerical calculations should be performed on nominal or ordinal data.
Interval and ratio scales use numerical values to quantify the size of an observation and the data resulting from these types of measurement is quantitative in nature. This makes interval and ratio data suitable for analyses that require calculations.
The difference between these scales lies in the manner in which the categories or values that make up a scale are related to each other.
Each new level in the hierarchy places an additional restriction on the relationship between the categories or values that make up the scale.