Typology
Stevens proposed his typology in a 1946 Science article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval" and "ratio", unifying both qualitative (which are described by his "nominal" type) and quantitative (to a different degree, all the rest of his scales). The concept of scale types later received the mathematical rigour that it lacked at its inception with the work of mathematical psychologists Theodore Alper (1985, 1987), Louis Narens (1981a, b) and R. Duncan Luce (1986, 1987, 2001). As Luce (1997, p. 395) stated:
| “ | S. S. Stevens (1946, 1951, 1975) claimed that what counted was having an interval or ratio scale. Subsequent research has given meaning to this assertion, but given his attempts to invoke scale type ideas it is doubtful if he understood it himself… no measurement theorist I know accepts Stevens' broad definition of measurement… in our view, the only sensible meaning for 'rule' is empirically testable laws about the attribute. | ” |
| Scale type |
Logical/math operations allowed |
Examples: Variable name (data values) |
Measure of central tendency |
Qualitative or Quantitative | |
| 1 | Nominal | =/≠ | Dichotomous: Gender (male vs. female) Non-dichotomous: Nationality (American/Chinese/etc) |
Mode | Qualitative |
| 2 | Ordinal | =/≠ ; | Dichotomous: Health (healthy vs. sick), Truth (true vs. false), Beauty (beautiful vs. ugly) Non-dichotomous: Opinion ('completely agree'/ 'mostly agree'/ 'mostly disagree'/ 'completely disagree') |
Median | Qualitative |
| 3 | Interval | =/≠ ; ; +/− | Date (from 9999 BC to 2013 AD) Latitude (from +90° to −90°) |
Arithmetic Mean | Quantitative |
| 4 | Ratio | =/≠ ; ; +/− ; ×/÷ | Age (from 0 to 99 years) |
Geometric Mean | Quantitative |
Read more about this topic: Numerical Data