Page 3: definitions of scales

Definitions of Scales: 
The first empirical task is measurement.   There are four measurement scales which differ in the type of quantitative information they provide.

1. Nominal scales:   In nominal scales, numbers are used as labels.  They convey no quantitative information about an underlying attribute.  Instead, they provide categorical information.  All you can say about nomially scaled scores is whether or not they are the same (that is, belonging to the same category) or different (that is, belonging to different categories).

For example, the attribute of sex may be numerically coded  using 0s and 1s, with 0 labeling males and 1 labeling females.  Or the attribute of religious affiliation may be numerically coded with 0 corresponding to Protestant, 1 corresponding to Catholic, 2 corresponding to Jewish, and so on.

Example:

          male = 0                                                           female = 1
                                         
 
 
 

2. Ordinal Scales:   In addition to saying whether scores are the same or different, numbers on an ordinal scale convey information about magnitude.  You can say whether or not two scores are equivalent (i.e., tied) and in addition, you can rank order scores such that one score can represent a greater or a lesser amount of an attribute than another score.

Example: Order of finish in a foot race to measure running ability:

First place >>>>>>>>>>>>>>>>>>>>>>>> Last place
 
 


3. Interval Scales: In addition to providing information about equivalence and relative magnitude of an attribute, interval scales tell us how much greater or less one score is than another score. In interval scales, each unit of measure represents a constant amount of attribute. In other words, the SIZE OF THE INTERVALS BETWEEN SCORES IS CONSTANT AND MEANINGFUL!!!!  Moreover, in interval scales, 0 does not mean the complete absence of an attribute.

Example: Degrees Celsius on a thermometer is a measurement of heat. The unit of measure is a degree, and each degree stands for a constant amount of heat throughout the temperature range.  Because the amount of heat measured by each degree is the same throught the temperature range, the difference in temperature between -15 degrees Celsius and 0 degrees Celsius is exactly the same as the difference between 80 degrees Celsius and 95 degrees Celsius.
 
 
Note that zero degrees Celsius does not indicate a complete absence of heat

 
 

** -15 degs Celsius  is 45 degrees cooler than +30 degs Celsius**


4. Ratio Scales:   Ratio scales are interval scales with an absolute zero point.  Thus, in addition to providing information about the difference between two persons or things in the amount of an attribute they have, ratio scales allow us to make statements about the ratio of an attribute that one person or thing has relative to another.   That is, with ratio scales statements such as 'one pencil’s length is twice that of another pencil' are meaningful.

PENCIL A

PENCIL B
 

In other words,the zero point for a ratio scale, such as length measured in centimeters, is non arbitrary.


For most basic statistics, the distinction between interval and ratio level measurement is not that important .