Measurement

The term number does not necessarily mean numbers that can be added, subtracted, multiplied or divided. Instead, it means numbers that are used as symbols to represent certain characteristics like age, income, the height of an object/person, etc. As a student, your student number identifies you. Assigning numbers to observations using an experiment is measurement. There are four levels of measurement, each with its own characteristics. From the weakest to the strongest. The analysis you carry out depends on the type of scale used to measure the characteristics that interest you. The four levels of measurement are:

Nominal Scale: Also known as a categorical level, this is the weakest type of measurement. Responses are classified into a number of distinct categories, with no order or value implied. Numbers or symbols are used to identify groups to which various observations belong, e.g. in counting males and females, the male group can be assigned a code 1 and the females a code 2. These nominally scaled numbers serve only as a label for a group, and the measurement consists of placing the data in the correct group. No arithmetic operations can be performed with such numbers, other than counting the groups and the number of elements falling into each group.

Ordinal Scale: This is the second weakest of the scales. The categories into which objects are grouped are ranked in some order using numbers or symbols, e.g. income level such as low, medium or high. Items can be classified not only as to whether they share some characteristic with another item but also as to whether they have more or less of this characteristic. The ordinal scale, however, certainly does not tell us how much more or less. The permissible analysis methods for ordinal data include those for nominal data, as well as techniques generally associated with the ordering of observations.

Interval Scale: This scale considers both the difference between measurements and their ordering. Temperature is a classic example of an interval scale. An increase on the centigrade scale between 10° and 20°, is the same as the increase between 30° and 40°. However, heat cannot be measured in absolute terms (0°C does not mean any heat) and it is not possible to say that 40° is twice as hot as 20°. This lack of an absolute zero sometimes causes difficulties in interpreting interval-scale data. Arithmetic operations can be performed on the difference between numbers, but not on the numbers themselves.

Ratio Scale: Only with the ratio scale can arithmetic operations be performed on the numerical values themselves. It is identical to the interval scale, with the additional characteristic of starting from zero. Money is an example of the ratio scale of measurement. The zero points are meaningful – at zero you have none, and R10 is twice as much as R5.

Now that we are familiar with the concept of measuring scales and variables, we can conclude that a qualitative variable is always the result of a nominal scale. Interval and ratio scales always produce quantitative data. The ordinal scale may produce either quantitative or qualitative data.