The data scale of a parameter is given by the statistic attributes of the values.
- nominal: Unordered set (only = or != relations)
Example: film titles.
- ordinal: Ordered set (=, !=, <, and > relations)
Example: film ratings.
- discrete: Numeric range (Integer, arithmetic possible)
- continuous: Numeric range (Real/float numbers, arithmetic possible)
Example: film length.
- binary: true or false (Boolean arithmetic)
Example: film available.
Note: Other often used terms in relation to data types are qualitative, quantitative, and categorical. Whereas qualitative subsumes nominal and ordinal, quantitative subsumes discrete and continuous, and categorical might be nominal, ordinal, or discrete data.
Nominal scales only have one formal property: category. Names of computer files are an example of nominal scales: they only discriminate between different entities but have no information about magnitudes, intervals, and ratios. Ordinal scales have two formal properties: category and magnitude. The activity levels of computer files are an example of ordinal scales: the activity level of a "hot" file is different from that of a "cold" file (category) and a "hot" file is more active than a "cold" file (magnitude). However, the activity levels themselves tell us nothing about the interval differences and ratios between the activity levels. Interval scales have three formal properties: category, magnitude, and equal interval. Time is an example of interval scales: 02:00 is different from 22:00 (category), 14:00 is later than 09:00 (magnitude), and the difference between 15:00 and 14:00 is the same as that between 09:00 and 08:00 (equal interval). However, time does not have an absolute zero. Thus, we cannot say that 10:00 is twice as late as 05:00. Ratio scales have all of the four formal properties: category, magnitude, equal interval, and absolute zero. The sizes of computer files are an example of ratio scales: 1K is different from 2K (category), 10K are larger than 5K (magnitude), the difference between 10K and 11K is the same as the difference between 100K and 101K (equal interval), and 0K means the nonexistence of size (absolute zero). For file sizes, we can say that 10K are twice as large as 5K.
Table 1: The Formal Properties of Scales
|Formal Properties||Scale Types|
|Example||file size||time||activity level||file name|
Source: [Zhang, 1996]
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- [Zhang, 1996] Zhang, J. 1996. A representational analysis of relational information displays. Int. J. Hum.-Comput. Stud. 45, 1 (Jul. 1996), 59-74. DOI= http://dx.doi.org/10.1006/ijhc.1996.0042