# Qualitative Variables

### From MM*Stat International

English |

Português |

Français |

Español |

Italiano |

Nederlands |

## Nominal Scale

The most primitive scale, one that is only capable of expressing whether two values are equal or not, is the nominal scale. It is purely qualitative. If an experiment’s sample space consists of categories without a natural ordering, the corresponding random variable is nominally scaled. The distinct numbers assigned to outcomes merely indicate whether any two outcomes are equal or not. For example, numbers assigned to different political opinions may be helpful in compiling results from questionnaires. Yet in comparing two opinions we can only relate them as being of the same kind or not. The numbers do not establish any ranking. Variables with exactly two mutually exclusive outcomes are called binary or dichotomous variables. If the indicator numbers assigned convey information about the ranking of the categories, a binary variable might also be regarded as ordinally scaled. If the categories (events) constituting the sample space are not mutually exclusive, i.e. one statistical element can correspond to more than one category, we call the variable cumulative. For example, a person might respond affirmatively to different categories of professional qualifications. But there cannot be more than one current full-time employment (by definition).

## Ordinal Scale

If the numbers assigned to measurements express a natural ranking, the variable is measured on an ordinal scale. The distances between different values cannot be interpreted—a variable measured on an ordinal scale is thus still somehow non-quantitative. For example, school marks reflect different levels of achievement. There is, however, usually no reason to regard a work receiving a grade of ’4’ as twice as good as one that achieved a grade of ’2’. As the numbers assigned to measurements reflect their ranking relatively to each other, they are called rank values. There are numerous examples for ordinally scaled variables in psychology, sociology, business studies etc. Scales can be designed attempting to measure such vague concepts as ‘social status’, ‘intelligence’, ‘level of aggression’ or ‘level of satisfaction’.