Levels of Measurement
In artificial-intelligence, you can end up dealing with all sorts of data. For example —
- maybe you are working with photos of people's faces;
- maybe you are creating a list of city names of cities in the Near East;
- maybe you have a list of blood types for all the patients that have visited the hospital;
- maybe you are working with hospital patient data about how severe their pain was — ex: "no pain", "mild pain" , "moderate pain", "it hurts bad", and "OMF!G, this is the worst pain I have ever felt!";
- maybe you are looking at student test scores, graded oon a curve;
- maybe you are recording the birth order (i.e., 1st child, 2nd child, 3rd child, etc) of all the people who work in a company;
- maybe you are have temperature<.em> records in °C (degree celsius);
- maybe you are looking at the year every customer of a company was born;
- maybe you are recording the heights of all the children in an elementary school;
- maybe you are collecting the prices of houses in the city of Isfahan;
- maybe you are are looking the number of photo each person takes every day on their mobile-phone;
- etc etc etc.
Some Differences
Some of these data are very different than each other.
For example — if the price of one house is $1,000,000 and the price of another house is $500,000, then I can say the price of the first house is 2× (two times) bigger than the first. (Since $1,000,000 = 2 × $500,000.)
But it is nonsense to say — 2 × type O+ blood. There is no concept of multiplying blood types.
The same is true for city names. It is nonsense to say — 5 × the city of Vancouver.
Types of Data
The levels of measurement are a way of understanding these different types of data.
The levels of measurement are a way of categorizing a
nominal data ,ordinal data ,interval data , andratio data .
Ratio Data
Interval Data
Ordinal 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:
- female
- male
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 |