# criteria and levels of measurement

## criteria and levels of measurement

the rules which govern the assignment of an appropriate value, code or score to an observed phenomenon. The most widely used classification is that devised by Stevens (1946,1951) who identified four levels of measurement –*nominal, ordinal, interval*and

*ratio*– distinguished according to their ordering and distance properties.

In *nominal-level measurement * each value represents a distinct category, and the value is merely a label or name. Values are assigned to the variable without reference to the ordering or distances between categories, in much the same sense that people have forenames such as Thomas, Richard, Catherine and Martha. Thus, nominal level measures lack many of the properties which real numbers possess, and it is not possible to add, subtract, multiply and divide such variables.

In *ordinal-level measurement values * are arranged in a rank order, such that if *a * is greater than *b * and *b * is greater than *c, * then it follows that *a * is also greater than *c, * although ordinal-level measurements give no indication of the relative distances between categories. For example, political parties might be arranged on a scale ranking from left-wing to right-wing, and although it is possible to say (in the UK) that the Labour Party is more left-wing than the Liberal Democratic Party, which in turn is more left-wing than the Conservative Party, we do not know what the *relative * distances are between these parties.

*Interval-level measurements * are an extension of ordinal-level variables except that the distances between categories are now fixed and equal. The Celsius temperature scale is an example of such a variable in that a change in temperature from say 2° to 3° represents the same magnitude of change as an increase in temperature from 64° to 65°C. However, interval-level scales are purely artificial constructions and the *zero point * is not inherently determined but, rather, is defined in terms of an arbitrarily agreed-upon definition. In consequence, the zero point, and even negative values on such scales, can represent real values. For example, it is possible to have a temperature of 0 °C and temperatures below this value. Because of their artificial and arbitrary nature, interval scales lack the property of proportionateness, and, in consequence, for example, 20 °C is not twice as hot as 10 °C.

Finally, *ratio-level measurements * make use of real numbers, and the distances between categories are fixed, equal and proportionate (Nachmias and Nachmias, 1976). The zero is now naturally defined and because of this *ratio comparisons * can now be made. For example, a two-metre-tall man has twice the height of a one-metre-tall boy

The importance of Stevens’ classification is that the statistical tests which it is permissible to use are determined by the variable type. Arranging Stevens’ variables in order – nominal, ordinal, interval and ratio – it can be shown that a statistical test which can be applied to a lower-level variable can also be applied to a higher-level variable. Very few statistical tests can be undertaken on a nominal-level variable, whilst any statistical test can be applied to a ratio-interval measure. Most variables which are commonly employed in the social sciences are of a nominal or ordinal nature, and in consequence only a limited number of tests can be applied to them. In the case of ordinal variables, for example, no statistical tests which involve calculating the MEAN are permissable. However, given the more sophisticated tests which are available, many social scientists prefer to use statistical tests which involve the calculation of the mean and STANDARD DEVIATION, although they are only fully justified with higher-level measurements. Laboriz (1970) and Taylor (1983) have undertaken a series of statistical tests on the validity of this approach and have concluded that it is generally acceptable, provided that the ordinal variables used are not of a dichotomous (see below) or trichotomous nature.

Other social scientists have attempted to elaborate upon Stevens’ schema. Fixed and ratio-interval data are often grouped together and called *continuous * data. Finally, *dichotomous * variables (which can take only one of two values, e.g. sex) are often treated as a separate level of measurement in their own right because they can be treated as nominal, ordinal, or fixed-interval measures, depending upon circumstances. See also MEASUREMENT BY FIAT.