1.3 Level of Measurement

Levels of measurement (aka. scales of measurement) are used to describe the type of data collected. The levels of measurement are nominal, ordinal, interval, and ratio, where the latter three are also called Metrics. Nominal and ordinal scales are used to describe categorical data. Interval and ratio scales are used to describe continuous data. The level of measurement is important because it determines the type of statistical analysis that can be performed on the data. For example, a nominal variable can be used to create a contingency table, but it cannot be used to create a regression model. The level of measurement is also important because it determines the type of statistical test that can be performed on the data. For example, a nominal variable can be used to create a chi-square test, but it cannot be used to create a t-test.

• Nominal: the data can only be categorized, e.g., gender.
• Ordinal: the data can be categorized and ranked, e.g., education level.
• Interval: the data can be categorized, ranked, and the difference between the data can be measured, e.g., temperature.
• Ratio: the data can be categorized, ranked, the difference between the data can be measured, and the data can be used as a zero point, e.g., age.

Data type	Measures of central tendency	Measures of variability
Nominal	Mode	None
Ordinal	Mode, Median	Range, Interquartile range
Interval	Mode, Median, Arithmetic mean	Range, Interquartile range, Standard deviation, Variance
Ratio	Mode, Median, Arithmetic mean, Geometric mean	Range, Interquartile range, Standard deviation, Variance, Relative standard deviation