Ratio Scale

True Zero Point

Variables measured at the ratio-scale level have equal distances between attributes and a true zero point. The score of zero in ratio-scale variables indicates the absence or complete lack of an attribute. The variable number of vehicles owned in the past 5 years is an example of a ratio-scale variable. A score of zero for this variable means the respondent owned no vehicles in the past 5 years.

Similarly, it is possible for respondents to have zero years of work experience, no children, a score of zero on a midterm exam, zero dollars in a savings account, or zero people living below the poverty line. These are all examples of ratio-scale variables.

The true zero point also makes a ratio-scale variable more precise than an interval-scale variable. The true zero point allows ratio scale variables to make statements about the ratio of attributes. It is possible to multiply and divide the attributes of a ratio-scale variable. For example, it is possible to say that four vehicles are twice as many as two vehicles in the variable number of vehicles owned in the past 5 years.

Similarly, for the variable number of years of work experience, those who have 3 years of work experience have half as many years of work experience as those who have 6 years of work experience. For the variable amount in a savings account, $1,500 is 3 times as much savings as $500 or one third as much savings as $4,500. In the variable proportion of people living below the poverty line, areas that have 3,000 people living below the poverty line have twice as many people living below the poverty line as areas that have 1,500 people living below the poverty line.

Mathematical Operations

One advantage, and perhaps the most important advantage, of the ratio scale is suitability for all mathematical operations. Data measurement on the ratio scale permits all mathematical operations to be used, including addition, subtraction, multiplication, division, and square roots. The use of all mathematical operations in turn permits the use of most statistical techniques for data measured on the ratio scale. There are many statistical techniques that are not appropriate for data measured at the nominal-, ordinal-, or interval-scale level but that are appropriate for the ratio-scale level, such as correlation, regression, factor analysis, and time-series analysis.

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