The frame into which we wish to make everything fit is one of our own construction; but we do not construct it at random, we construct it by measurement so to speak; and that is why we can fit the facts into it without altering their essential qualities. (Poincare 1952: xxv)
Measurement is central to any enquiry. In addition to the ideology and philosophy that underpin each mode of enquiry, the most significant difference between qualitative and quantitative research studies is in the types of measurement used in collecting information from the respondents. Qualitative research mostly uses descriptive statements to seek answers to the research questions, whereas in quantitative research these answers are usually sought on one of the measurement scales (nominal, ordinal, interval or ratio). If a piece of information is not collected using one of the scales at the time of data collection, it is transformed into variables by using these measurement scales at the time of analysis. Measurement on these scales could be either in the form of qualitative categories or through a precise unit of measurement. Those scales which have a unit of measurement (interval and ratio) are considered to be more refined, objective and accurate. On the other hand, nominal and ordinal scales are considered subjective and hence not as accurate as they do not have a unit of measurement per se. The greater the refinement in the unit of measurement of a variable, the greater the confidence placed in the findings by others, other things being equal. One of the main differences between the physical and the social sciences is the units of measurement used and the degree of importance attached to them. In the physical sciences measurements have to be absolutely accurate and precise, whereas in the social sciences they may vary from the very subjective to the very quantifiable. Within the social sciences the emphasis on precision in measurement varies markedly from one discipline to another. An anthropologist normally uses very ‘subjective’ units of measurement, whereas an economist or an epidemiologist emphasises ‘objective’ measurement.
There are two main classification systems in the social sciences for measuring different types of variable. One was developed by S. S. Stevens (in 1946) and the other by Duncan (in 1984). According to Smith (1991: 72), ‘Duncan (1984) has enumerated, in increasing order of interest to scientists, five types of measurement: nominal classification, ordinal scaling, cardinal scaling, ratio scaling, and probability scaling’. Duncan writes about Stevens’s classification as follows:
The theory of scale types proposed in 1946 by S S Stevens focused on nominal, ordinal, interval, and ratio scales of measurement. Some of his examples of these types — notably those concerning psychological test scores — are misleading. (1984: viii)
However, Bailey considers that ‘S S Stevens constructed a widely adopted classification of levels of measurement’ (1978: 52). As this book is written for the beginner and as Stevens’s classification is simpler, it is this that is used for discussion in this chapter. Stevens has classified the different types of measurement scale into four categories:
- nominal or classificatory scale;
- ordinal or ranking scale;
- interval scale;
- ratio scale.
1. The nominal or classificatory scale
A nominal scale enables the classification ofindividuals, objects or responses based on a common/ shared property or characteristic. These people, objects or responses are divided into a number of subgroups in such a way that each member of the subgroup has a common characteristic. A variable measured on a nominal scale may have one, two or more subcategories depending upon the extent of variation. For example, ‘water’ and ‘taxi’ have only one subgroup, whereas the variable ‘gender’ can be classified into two subcategories: male and female. Political parties in Australia can similarly be classified into four main subcategories: Labor, Liberal, Democrats and Greens. Those who identify themselves, either by membership or belief, as belonging to the Labor Party are classified as ‘Labor’, those identifying with the Liberals are classified as ‘Liberal’, and so on. The name chosen for a subcategory is notional, but for effective communication it is best to choose something that describes the characteristic of the subcategory.
Classification by means of a nominal scale ensures that individuals, objects or responses within the same subgroup have a common characteristic or property as the basis of classification. The sequence in which subgroups are listed makes no difference as there is no relationship among subgroups.
2. The ordinal or ranking scale
An ordinal scale has all the properties of a nominal scale — categorising individuals, objects, responses or a property into subgroups on the basis of a common characteristic — but also ranks the subgroups in a certain order. They are arranged in either ascending or descending order according to the extent that a subcategory reflects the magnitude of variation in the variable. For example, income can be measured either quantitatively (in dollars and cents) or qualitatively, using subcategories: ‘above average’, ‘average’ and ‘below average’. (These categories can also be developed on the basis of quantitative measures, for example below $10 000 = below average, $10 000—$25 000 = average and above $25 000 = above average.) The subcategory ‘above average’ indicates that people so grouped have more income than people in the ‘average’ category, and people in the ‘average’ category have more income than those in the ‘below average’ category. These subcategories of income are related to one another in terms of the magnitude of people’s income, but the magnitude itself is not quantifiable, and hence the difference between ‘above average’ and ‘average’ or between ‘average’ and ‘below average’ subcategories cannot be ascertained. The same is true for other variables such as socioeconomic status and attitudes measured on an ordinal scale.
Therefore, an ordinal scale has all the properties/characteristics of a nominal scale, in addition to its own. Subcategories are arranged in order of the magnitude of the property/characteristic. Also, the ‘distance’ between the subcategories is not equal as there is no quantitative unit of measurement.
3. The interval scale
An interval scale has all the characteristics of an ordinal scale; that is, individuals or responses belonging to a subcategory have a common characteristic and the subcategories are arranged in an ascending or descending order. In addition, an interval scale uses a unit of measurement that enables the individuals or responses to be placed at equally spaced intervals in relation to the spread of the variable. This scale has a starting and a terminating point and is divided into equally spaced units/intervals. The starting and terminating points and the number of units/intervals between them are arbitrary and vary from scale to scale.
Celsius and Fahrenheit scales are examples of an interval scale. In the Celsius system the starting point (considered as the freezing point) is 0°C and the terminating point (considered as the boiling point) is 100°C. The gap between the freezing and boiling points is divided into 100 equally spaced intervals, known as degrees. In the Fahrenheit system the freezing point is 32°F and the boiling point is 212°F, and the gap between the two points is divided into 180 equally spaced intervals. Each degree or interval is a measurement of temperature — the higher the degree, the higher the temperature. As the starting and terminating points are arbitrary, they are not absolute; that is, you cannot say that 60°C is twice as hot as 30°C or 30°F is three times hotter than 10°F. This means that while no mathematical operation can be performed on the readings, it can be performed on the differences between readings. For example, if the difference in temperature between two objects, A and B, is 15°C and the difference in temperature between two other objects, C and D, is 45°C, you can say that the difference in temperature between C and D is three times greater than that between A and B. An attitude towards an issue measured on the Thurstone scale is similar. However, the Likert scale does not measure the absolute intensity of the attitude but simply measures it in relation to another person.
The interval scale is relative; that is, it plots the position of individuals or responses in relation to one another with respect to the magnitude of the measurement variable. Hence, an interval scale has all the properties of an ordinal scale, and it has a unit of measurement with an arbitrary starting and terminating point.
4. The ratio scale
A ratio scale has all the properties of nominal, ordinal and interval scales and it also has a starting point fixed at zero. Therefore, it is an absolute scale — the difference between the intervals is always measured from a zero point. This means the ratio scale can be used for mathematical operations. The measurement of income, age, height and weight are examples of this scale. A person who is 40 years of age is twice as old as a 20-year-old. A person earning $60 000 per year earns three times the salary of a person earning $20 000.
Source: Kumar Ranjit (2012), Research methodology: a step-by-step guide for beginners, SAGE Publications Ltd; Third edition.