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Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal , ordinal , interval , and ratio .
A nominal variable, or nominal group, is a group of objects or ideas collectively grouped by a particular qualitative characteristic. [3] Nominal variables do not have a natural order, which means that statistical analyses of these variables will always produce the same results, regardless of the order in which the data is presented. [1] [3]
If for years 1 and 2 (possibly a span of 20 years apart), the nominal wage and price level P of goods are respectively nominal wage rate: $10 in year 1 and $16 in year 2 price level: 1.00 in year 1 and 1.333 in year 2, then real wages using year 1 as the base year are respectively: $10 (= $10/1.00) in year 1 and $12 (= $16/1.333) in year 2.
For example, both 1 ⁄ 2 inch and 15 millimetres (0.59 in) copper pipe is actually the same pipe which has a nominal internal diameter of 1 ⁄ 2 an inch and a nominal external diameter of 15 millimetres [6] (diameter is always internal in the imperial measurement system and always external in metric).
For example, a scaling technique might involve estimating individuals' levels of extraversion, or the perceived quality of products. Certain methods of scaling permit estimation of magnitudes on a continuum, while other methods provide only for relative ordering of the entities. The level of measurement is the type of data that is measured.
For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale). Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens ...
[1]: 2 These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. [2] It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute. [3]
Descriptive statistics describe a sample or population. They can be part of exploratory data analysis. [11] The appropriate statistic depends on the level of measurement. For nominal variables, a frequency table and a listing of the mode(s) is sufficient.