Levels of Measurement
The levels of measurement are a way of categorizing a data as one of four different categories:
- nominal data,
- ordinal data,
- interval data, and
- ratio data.
Nominal Data
An example of nominal data is blood types:
- type A+
- type A-
- type B+
- type B-
- type AB+
- type AB-
- type O+
- type O-
Another example of nominal data is sex:
Another example of nominal data is family names:
- Alves
- Beg
- Chen
- Cho
- Choi
- da Silva
- Dickson
- dos Santos
- Esfahani
- Fernández
- Ferreira
- García
- Jung
- Kang
- Kerr
- Kim
- Krempeaux
- Li
- Liu
- Martin
- Müller
- Pahlavi
- Park
- Parsi
- Pereira
- Rodríguez
- Safavi
- Sasani
- Wang
- Yun
- Zhang
- etc
Another example of nominal data is hair color:
- brown
- black
- blond
- gray
- red
- etc
Another example of nominal data is cities:
- Beijing
- Bangalore
- Bangkok
- Bogotá
- Buenos Aires
- Cairo
- Chennai
- Chicago
- Chongqing
- Dallas
- Delhi
- Dhaka
- Guangzhou
- Hyderabad
- Kinshasa
- Kolkata
- Isfahan
- Istanbul
- Jakarta
- Karachi
- Lagos
- Lahore
- Lima
- London
- Los Angeles
- Moscow
- Nagoya
- New York City
- Osaka
- Manila
- Mexico City
- Mumbai
- Paris
- Rio de Janeiro
- São Paulo
- Seoul
- Shanghai
- Shenzhen
- Tehran
- Tianjin
- Tokyo
- Toronto
- Vancouver
- etc
Operations
One way of understanding the levels of measurement is — what type of operations are meaningful and valid for that type of data‽
Here is a table that summarizes what operations are and are notmeaningful and valid for each levels of measurement category:
|
nominal |
ordinal |
interval |
ratio |
| can × and ÷ ? |
no |
no |
no |
YES |
| can + and - ? |
no |
no |
YES |
YES |
| can < and > ? |
no |
YES |
YES |
YES |
| can = and ≠ ? |
YES |
YES |
YES |
YES |