The type of data collected determines the appropriate measurement scale, and the measurement scale, in turn, determines the appropriate statistical procedure for analyzing particular data and drawing conclusions from that data. Each type of measurement scale has a specific use.
Nominal scales. Nominal scales are composed of sets of categories in which objects are classified. For example, a nominal scale dealing with household pets might include the categories dogs, cats, birds, and fish. Data used in the construction of a nominal scale are frequency data, the number of subjects in each category (in this case, the number of animals for each type of pet).
Ordinal scales. Ordinal scales indicate the order of the data according to some criterion. For example, a researcher might ask people to rank their preference for types of household pets, with 1 as the most preferred and 4 as the least preferred (resulting in, perhaps, 1‐dogs, 2‐cats, 3‐birds, 4‐fish). Ordinal scales tell nothing about the distance between units of the scale (for example, although dogs may be preferred to cats, no information is available about the extent of that preference) and supply information only about order of preference.
Interval scales. Interval scales have equal distances between scale units and permit statements to be made about those units as compared to other units (that is, one unit may be a certain number of units higher or lower than another), but they do not allow conclusions that one unit is a particular multiple of another because on interval scales there is no zero. That is, the scale does not allow for the complete absence of the phenomenon being measured. For example, if you refer to the interval scale used on a thermometer, you can say that 88 degrees is 2 degrees higher than 86 degrees, but you cannot accurately say that 88 degrees is twice as hot as 44 degrees because there is never a situation of no heat at all. (The zero on a thermometer doesn't indicate a complete lack of heat, only one more unit on the scale, which continues downward.) Interval scales, then, permit a statement of “more than” or “less than” but not of “how many times more.”
Ratio scales. Ratio scales have equal distances between scale units as well as an absolute zero. If you're measuring the height of two trees and tree A is 36 inches tall and tree B is 72 inches tall, you can accurately say that B is twice as tall as A. There is a condition of zero height. Most measures encountered in daily living are based on a ratio scale.
Continuous and discontinuous scales. Measures may also be categorized according to continuity and discontinuity. A continuous scale is one in which the variable under consideration can assume an infinite number of values. A person's height, for example, might be expressed in an infinite number of ways, ranging from feet, to inches, to tenths of inches, to hundredths of inches, and so forth according to how small or large a measurement one wants to make. On the other hand, discontinuous, or discrete, scales express the measurement of the variable under consideration in a finite number of ways, as, for example, in a frequency distribution such as the number of students in a psychology department or the number of players on a team.