Before looking at any statistics, we need to review the concept of scales of measurement. Whenever a variable is studied, the researcher must create an operational definition of the variable and devise two or more levels of the variable. Recall from Chapter 5 that the levels of the variable can be described using one of four scales of measurement: nominal, ordinal, interval, and ratio. The scale used determines the types of statistics that are appropriate when the results of a study are analyzed. Also recall that the meaning of a particular score on a variable depends on which type of scale was used when the variable was measured or manipulated.
The levels of nominal scale variables have no numerical, quantitative properties. The levels are simply different categories or groups. Most independent variables in experiments are nominal, for example, as in an experiment that compares behavioral and cognitive therapies for depression. Variables such as gender, eye color, hand dominance, college major, and marital status are nominal scale variables; left-handed and right-handed people differ from each other, but not in a quantitative way.
Variables with ordinal scale levels exhibit minimal quantitative distinctions. We can rank order the levels of the variable being studied from lowest to highest. The clearest example of an ordinal scale is one that asks people to make rank-ordered judgments. For example, you might ask people to rank the most important problems facing your state today. If education is ranked first, health care second, and crime third, you know the order but you do not know how strongly people feel about each problem: Education and health care may be very close together in seriousness with crime a distant third. With an ordinal scale, the intervals between each of the items are probably not equal.
Interval scale and ratio scale variables have much more detailed quantitative properties. With an interval scale variable, the intervals between the levels are equal in size. The difference between 1 and 2 on the scale, for example, is the same as the difference between 2 and 3. Interval scales generally have five or more quantitative levels. You might ask people to rate their mood on a 7-point scale ranging from a “very negative” to a “very positive” mood. There is no absolute zero point that indicates an “absence” of mood.
Page 244In the behavioral sciences, it is often difficult to know precisely whether an ordinal or an interval scale is being used. However, it is often useful to assume that the variable is being measured on an interval scale because interval scales allow for more sophisticated statistical treatments than do ordinal scales. Of course, if the measure is a rank ordering (for example, a rank ordering of students in a class on the basis of popularity), an ordinal scale clearly is being used.
Ratio scale variables have both equal intervals and an absolute zero point that indicates the absence of the variable being measured. Time, weight, length, and other physical measures are the best examples of ratio scales. Interval and ratio scale variables are conceptually different; however, the statistical procedures used to analyze data with such variables are identical. An important implication of interval and ratio scales is that data can be summarized using the mean, or arithmetic average. It is possible to provide a number that reflects the mean amount of a variable—for example, the “average mood of people who won a contest was 5.1” or the “mean weight of the men completing the weight loss program was 187.7 pounds.”
Scales of measurement have important implications for the way that the results of research investigations are described and analyzed. Most research focuses on the study of relationships between variables. Depending on the way that the variables are studied, there are three basic ways of describing the results: (1) comparing group percentages, (2) correlating scores of individuals on two variables, and (3) comparing group means.