## 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 |