Scales of Measurement
One of the most important schemes for classifying a variable involves its scale of measurement. Data generally fall within four different scales of measurement: nominal; ordinal; ratio; and interval. Before analyzing a dataset, it is important to determine which scales of measurement were used because certain types of statistical procedures require specific scales of measurement. In this text, each chapter that deals with a specific statistical procedure specifies what scale of measurement is required. The researcher must determine scales of measurement for study variables before selecting which statistical procedures to use.
Nominal Scales
A nominal scale is a classification system that places people, objects, or other entities into mutually exclusive categories. A variable measured along a nominal scale is a classification variable; it simply indicates the group to which each participant belongs. The examples of classification variables provided earlier (e.g., Sex and Ethnicity) also are examples of nominal-level variables; they tell us to which group a participant belongs but they do not provide any quantitative information. That is, the Sex variable identifies participants as either male or female but it does not tell us that participants possess more or less of a specific characteristic relative to others. However, the remaining three scales of measurement—ordinal, interval, and ratio—provide some quantitative information.
Ordinal Scales
Values on an ordinal scale represent the rank order of participants with respect to the variable being assessed. For example, the preceding table includes one variable called Rank that represents the rank ordering of participants according to their overall effectiveness as agents. Values for this ordinal scale represent a hierarchy of levels with respect to the construct of “effectiveness.” We know that the agent ranked 1 was perceived as being more effective than the agent ranked 2, that the agent ranked 2 was more effective than the one ranked 3, and so forth.
 | The information conveyed by an ordinal scale is limited because equal differences in scale values do not necessarily have equal quantitative meaning. For example, notice the following rankings: |
| Rank | Name |
|---|---|
| 1 | Bob |
| 2 | Pietro |
| 3 | Susan |
| 4 | LeMont |
| 5 | Saleem |
| 6 | Mack |
Notice that Bob was ranked 1 while Pietro was ranked 2. The difference between these two rankings is 1 (because 2 – 1 = 1), so there is one unit of difference between Bob and Pietro. Now notice that Saleen was ranked 5 while Mack was ranked 6. The difference between these two rankings is also 1 (because 6 – 5 = 1), so there is also 1 unit of difference between Saleem and Mack. Putting the two together, the difference in ranking between Bob and Pietro is equal to the difference in ranking between Saleem and Mack.
But, does this mean that the difference in overall effectiveness between Bob and Pietro is equal to the difference in overall effectiveness between Saleem and Mack? Not necessarily. It is possible that Bob was significantly superior to Pietro in effectiveness, while Saleem might have been only slightly superior to Mack. In fact, this appears to be the case. Whereas Bob had sold policies totaling $598,243, Pietro had sold $367,342 for a difference of $230,830 between the two. In contrast, the difference in sales between Saleem ($40,170) and Mack ($0) was only a faction of the difference between Bob and Pietro (i.e., $40,170 vs. $230,830). This example indicates that these rankings reveal very little about the quantitative differences between participants with regard to the underlying construct (effectiveness, in this case). An ordinal scale simply provides a rank order. Other scales of measurement are required to provide this added level of measurement.
Interval Scales
With an interval scale, equal differences between values have equal quantitative meaning. For this reason, it can be seen that an interval scale provides more quantitative information than an ordinal scale. A good example of interval measurement is the Fahrenheit scale used to measure temperature. With the Fahrenheit scale, the difference between 70 degrees and 75 degrees is equal to the difference between 80 degrees and 85 degrees. In other words, the units of measurement are equal throughout the full range of the scale.
However, the interval scale also has a limitation; it does not have a true zero point. A true zero point means that a value of zero on the scale represents zero quantity of the variable being assessed. It should be obvious that the Fahrenheit scale does not have a true zero point; when the thermometer reads 0 degrees Fahrenheit, that does not mean that there is absolutely no heat present in the environment.
Social scientists often assume that many of their man-made variables are measured on an interval scale. In the preceding study involving insurance agents, for example, you would probably assume that scores from the goal difficulty questionnaire constitute an interval-level scale (i.e., you would likely assume that the difference between a score of 50 and 60 is approximately equal to the difference between a score of 70 and 80). Many researchers would also assume that scores from an instrument such as an intelligence test are also measured at the interval level of measurement.
On the other hand, some researchers are skeptical that instruments such as these have true equal-interval properties and prefer to refer to them as quasi-interval scales (e.g., Likert-type scales to which respondents indicate their degree of agreement to a series of statements with a fixed number of response alternatives such as strongly disagree, disagree, neutral, agree, and strongly agree). Disagreements concerning the level of measurement with such instruments continue to be a controversial topic within the social sciences (i.e., whether scale responses ranging from strongly disagree to strongly agree constitute ordinal- or interval-level measurement).
It is clear that there is no true zero point with either of the preceding instruments. A score of 0 on the goal difficulty scale does not indicate the complete absence of goal difficulty, and a score of 0 on an intelligence test does not indicate the complete absence of intelligence. A true zero point can be found only with variables measured on a ratio scale.
Ratio Scales
Ratio scales are similar to interval scales in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point which gives them an additional property. With ratio scales, it is possible to make meaningful statements about the ratios between scale values. For example, the system of inches used with a common ruler is an example of a ratio scale. There is a true zero point with this system in which zero inches does, in fact, indicate a complete absence of length. With this scale, therefore, it is possible to make meaningful statements about ratios. It is appropriate to say that an object four inches long is twice as long as an object two inches long. Age, as measured in years, is also on a ratio scale as a 10-year old house is twice as old as a 5-year old house. Notice that it is not possible to make these statements about ratios with the interval-level variables discussed above. One would not say that a person with an IQ of 160 is twice as intelligent as a person with an IQ of 80.
Although ratio-level scales might be easiest to find when one considers the physical properties of objects (e.g., height and weight), they are also common in the type of research discussed in this text. For example, the study discussed previously included the variables for age and amount of insurance sold (in dollars). Both of these have true zero points and are measured as ratio scales.