Averages of Qualitative and Ranked Data

The central tendency for qualitative data can be described via the median or the mode, but not the mean.

Learning Objective

Categorize levels of measurement and identify the appropriate measures of central tendency.

Key Points

Qualitative data can be defined as either nominal or ordinal.
The nominal scale differentiates between items or subjects based only on their names and/or categories and other qualitative classifications they belong to.
The mode is allowed as the measure of central tendency for nominal data.
The ordinal scale allows for rank order by which data can be sorted, but still does not allow for relative degree of difference between them. The median and the mode are allowed as the measure of central tendency; however, the mean as the measure of central tendency is not allowed.
The median and the mode are allowed as the measure of central tendency for ordinal data; however, the mean as the measure of central tendency is not allowed.

Terms

quantitative
of a measurement based on some quantity or number rather than on some quality
qualitative
of descriptions or distinctions based on some quality rather than on some quantity
dichotomous
dividing or branching into two pieces

Full Text

Levels of Measurement

In order to address the process for finding averages of qualitative data, we must first introduce the concept of levels of measurement. In statistics, levels of measurement, or scales of measure, are types of data that arise in the theory of scale types developed by the psychologist Stanley Smith Stevens. Stevens proposed his typology in a 1946 Science article entitled "On the Theory of Scales of Measurement. " In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval" and "ratio", unifying both qualitative (which are described by his "nominal" type) and quantitative (to a different degree, all the rest of his scales).

Nominal Scale

The nominal scale differentiates between items or subjects based only on their names and/or categories and other qualitative classifications they belong to. Examples include gender, nationality, ethnicity, language, genre, style, biological species, visual pattern, and form.

The mode, i.e. the most common item, is allowed as the measure of central tendency for the nominal type. On the other hand, the median, i.e. the middle-ranked item, makes no sense for the nominal type of data since ranking is not allowed for the nominal type.

Ordinal Scale

The ordinal scale allows for rank order (1st, 2nd, 3rd, et cetera) by which data can be sorted, but still does not allow for relative degree of difference between them. Examples include, on one hand, dichotomous data with dichotomous (or dichotomized) values such as "sick" versus "healthy" when measuring health, "guilty" versus "innocent" when making judgments in courts, or "wrong/false" versus "right/true" when measuring truth value. On the other hand, non-dichotomous data consisting of a spectrum of values is also included, such as "completely agree," "mostly agree," "mostly disagree," and "completely disagree" when measuring opinion .

Ordinal Scale Surveys

An opinion survey on religiosity and torture. An opinion survey is an example of a non-dichotomous data set on the ordinal scale for which the central tendency can be described by the median or the mode.

The median, i.e. middle-ranked, item is allowed as the measure of central tendency; however, the mean (or average) as the measure of central tendency is not allowed. The mode is also allowed.

In 1946, Stevens observed that psychological measurement, such as measurement of opinions, usually operates on ordinal scales; thus means and standard deviations have no validity, but they can be used to get ideas for how to improve operationalization of variables used in questionnaires.

[ edit ]

Prev Concept

Which Average: Mean, Mode, or Median?

Measures of Relative Standing

Next Concept