In the department store project, numbers I through 10 were assigned to the 10 stores considered in the study (see Table 8.2). Thus store number 9 referred to Sears. This did not imply that Sears was in any way superior or inferior to Neiman Marcus, which was assigned the number 6. Any reassignment of the numbers, such as transposing the numbers assigned to Sears and Neiman Marcus, would have no effect on the numbering system, because the numerals did not reflect any characteristics of the stores. It is meaningful to make statements such as “75 percent of the respondents patronized store 9 (Sears) within the last month.” Although the average of the assigned numbers is 5.5, it is not meaningful to state that the number of the average store is 5.5
An ordinal scale is a ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic. An ordinal scale allows you to determine whether an object has more or less of a characteristic than some other object, but not how much more or less. Thus, an ordinal scale indicates relative position, not the magnitude of the differences between the objects, The object ranked first has more of the characteristic as compared to the object ranked second, but whether the object ranked second is a close second or a poor second is not known. The ordinal scales possess description and order characteristics but do not possess distance (or origin). Common examples of ordinal scales include quality rankings, rankings of teams in a tournament, socioeconomic class, and occupational status. In marketing research, ordinal scales are used to measure relative attitudes, opinions, perceptions and preferences. In the opening example, the ranlc order of the most admired companies represented an ordinal scale. Apple with a rank of I, was America’s most admired company.
Measurements of this type include “greater than” or “less than” judgments from the respondents
In an ordinal scale, as in a nominal scale, equivalent objects receive the same rank. Any series of numbers can be assigned that preserves the ordered relationships between the objects. For example. ordinal scales can be transformed in any way as long as the basic ordering of the objects is mainframe In other words. any monotonic positive (order-preserving) transformation of the scale is permissible. because the differences in numbers are void of any meaning other than order (see the following example). For these reasons, in addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles. It is meaningful to calculate percentile, quartile, median (Chapter 15), rank order correlation or other summary statistics from ordinal data.
In Table 8.2. a respondent’s preferences for the IO stores are expressed on a 7-point rating scale. We can see that although Sears received a preference rating of 6 and Wal·Mart a rating of 2, this does not mean that Sears is preferred three times as much as Wal-Mart. When the ratings are transformed to an equivalent II-to-l7 scale (next column). the ratings for these stores become 16 and 12. and the ratio is no longer 3 to I. In contrast, the ratios of preference differences are identical on the two scales. ‘The ratio of the preference difference between JCPenney and Wal-Mart to the preference difference between Neiman Marcus and Wal-Mart is 5 to 3 on both the scales
As a further illustration, Federation Internationale de Football Association (FIFA) uses ordinal and interval scaling to rank football teams of various countries
Scaling the Football World
‘The alphabets assigned to countries constitute a nominal scale, and the rankings represent an ordinal scale. whereas the points awarded denote an interval scale. Thus country G refers to Argentina. which was ranked 7 and received 1.230 points. Note that the alphabets assigned to denote the countries simply serve the purpo”<‘ of Identification and are not in any way related to their football-playing capabilities. Such information car. be obtained onl~ b) looking at the ranks. Thus. Croatia, ranked 5, played better than Turkey. ranked 10. The lower the rank. the better the performance. The ranks do not give any information on the magnitude of the differences between countries.” hich can be obtained only by looking at the points. Based on the points awarded. it can be S<.’Cn that Italy. w ith 1339 points. played only marginally better than Germany, with 1,329 points. The points help us to discern the magnitude of difference between countries receiving different ranks
All statistical techniques can be applied to ratio data. These include specialized statistics such as geometric mean. harmonic mean. and coefficient of variation. The four primary scales (discussed here) do not exhaust the measurement-level categories. It is possible to construct a nominal scale that provides partial information on order (the partially ordered scale). Likewise. an ordinal scale can convey partial information on distance. as in the case of an ordered metric scale. A discussion of these scales is beyond the scope of this text?
A Comparison of Scaling Techniques
The scaling techniques commonly employed in marketing research can be classified into comparative and non comparative scales (see Figure 8.2). Comparative scales involve the direct comparison of stimulus objects. For example, respondents might be asked whether they prefer Coke or Pepsi. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties. For this reason, comparative scaling is also referred to as nonmetric scaling. As shown in Figure 8.2, comparative scales include paired comparisons, rank order, constant sum scales, Qvsort, and other procedures.
The major benefit .of comparative scaling is that small differences between stimulus objects can be detected. As they compare the stimulus objects, respondents are forced to choose between them. In addition. respondents approach the rating task from the same known reference points. Consequently, comparative scales are easily understood and can be applied easily. Other advantages of these scales are that they involve fewer theoretical assumptions, and they also tend to reduce halo or carryover effects from one judgment to another. The major disadvantages of comparative scales include the ordinal nature of the data and the inability to generalize beyond the stimulus objects scaled. For instance, to compare RC Cola to Coke and Pepsi, the researcher would
In non comparative scales, also referred to as monadic or metric scales, each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled.f For example, ‘respondents may be asked to evaluate Coke on a l-to-S preference scale (1 = not at all preferred, 6 = greatly preferred). Similar evaluations would be obtained for Pepsi and RC Cola. As can be seen in Figure 8.2, noncomparative scales can be continuous rating or itemized rating scales. The itemized rating scales can be further classified as Likert, semantic differential, or Stapel scales. Non comparative scaling is the most
widely used scaling technique in marketing research. Given its importance. Chapter 9 is devoted to non comparative scaling. The rest of this chapter focuses on comparative scaling techniques