Levels of Measurement
+
+ The levels of measurement are a way of categorizing a
-
+
nominal data ,
+ ordinal data ,
+ interval data , and
+ ratio 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 | +