# Data Scale

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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)
Example:film year.
• 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.

Every dimension, whether it is a physical dimension such as the length of a bar or a more abstract dimension such as the amount of money, is on a certain type of scale. The scale of a dimension is the abstract measurement property of the dimension (see Krantz, Luce, Suppes, & Tversky, 1971; Narens, 1981; Stevens, 1946). Stevens identified four major types of scales: ratio, interval, ordinal, and nominal. Each type has one or more of the following formal properties: category, magnitude, equal interval, and absolute zero (see Table 1). Category refers to the property that the instances on a scale can be distinguished from each another. Magnitude refers to the property that one instance on a scale can be judged greater than, less than, or equal to another instance on the same scale. Equal interval refers to the property that the magnitude of an instance represented by a unit on the scale is the same regardless of where on the scale the unit falls. An absolute zero is a value which indicates that nothing at all of the property being represented exists.
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.
[Zhang, 1996]

Table 1: The Formal Properties of Scales

 Formal Properties Scale Types ratio interval ordinal nominal category yes yes yes yes magnitude yes yes yes no equal interval yes yes no no absolute zero yes no no no Example file size time activity level file name

Source: [Zhang, 1996]