Ordinal variable

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories is not known. 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 ordered categories. It also differs from interval and ratio scales by not having category widths that represent equal increments of the underlying attribute.

A well-known example of ordinal data is the Likert scale. An example of a Likert scale is:

Examples of ordinal data are often found in questionnaires: for example, the survey question "Is your general health poor, reasonable, good, or excellent?" may have those answers coded respectively as 1, 2, 3, and 4. Sometimes data on an interval scale or ratio scale are grouped onto an ordinal scale: for example, individuals whose income is known might be grouped into the income categories $0-$19,999, $20,000-$39,999, $40,000-$59,999, ..., which then might be coded as 1, 2, 3, 4, .... Other examples of ordinal data include socioeconomic status, military ranks, and letter grades for coursework.

Ordinal data analysis requires a different set of analyses than other qualitative variables. These methods incorporate the natural ordering of the variables in order to avoid loss of power. Finding a mean or standard deviation for ordinal data is often discouraged, but other methods such as median or mode should instead be used.

Stevens (1946) argued that, because the assumption of equal distance between categories does not hold for ordinal data, the use of means and standard deviations for description of ordinal distributions and of inferential statistics based on means and standard deviations was not appropriate. Instead, positional measures like the median and percentiles, in addition to descriptive statistics appropriate for nominal data (number of cases, mode, contingency correlation), should be used.Nonparametric methods have been proposed as the most appropriate procedures for inferential statistics involving ordinal data, especially those developed for the analysis of ranked measurements. However, use of parametric statistics for ordinal data may be permissible with certain caveats to take advantage of the greater range of available statistical procedures.

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