A Comparative Analysis of the Rotating Anchor Point and Magnitude Estimation Techniques in the Making of Children's Direct Similarity Judgments

Stuart Van Auken, University of Louisville
Subhash C. Lonial, University of Louisville
ABSTRACT - This study seeks to compare the efficacy of the rotating anchor point and magnitude estimation techniques in the making of children's direct similarity judgments. The rationale for such a comparison involves their inherent differences in scale orientation, task complexity and potential for data upgrading. Comparisons will be based on multidimensional scaling results; including global and individual goodness-of-fit, as well as stimulus map convergence.
[ to cite ]:
Stuart Van Auken and Subhash C. Lonial (1980) ,"A Comparative Analysis of the Rotating Anchor Point and Magnitude Estimation Techniques in the Making of Children's Direct Similarity Judgments", in NA - Advances in Consumer Research Volume 07, eds. Jerry C. Olson, Ann Abor, MI : Association for Consumer Research, Pages: 709-712.

Advances in Consumer Research Volume 7, 1980     Pages 709-712


Stuart Van Auken, University of Louisville

Subhash C. Lonial, University of Louisville


This study seeks to compare the efficacy of the rotating anchor point and magnitude estimation techniques in the making of children's direct similarity judgments. The rationale for such a comparison involves their inherent differences in scale orientation, task complexity and potential for data upgrading. Comparisons will be based on multidimensional scaling results; including global and individual goodness-of-fit, as well as stimulus map convergence.


The attainment of children's perceptual insights into various brands may represent an interesting area of challenge for marketers, consumer protection groups, and governmental agencies. This is because children, when contrasted to adults, probably have greater difficulty in recognizing and articulating their perceptual cues, or dimensions.

However, one may remedy the difficulty by using direct measures of brand similarity and multidimensional scaling (MDS). The resulting brand stimulus map(s), assuming an optimal and unique orientation of the coordinate axes, can then be subjected to a dimensional interpretation. This means that an attempt is made to interpret the evoked dimension(s), thus bypassing any need for respondent articulation. Basically, respondents can make similarity judgments although they may be unable to articulate their perceptual criteria.

Still, the usage of direct similarity judgments is not without problems. For example, respondents may become fatigued or lose interest because of task complexity. Such problems may be particularly acute with children as respondents. In fact, there is a persistent belief among consumer researchers that children's (attitude) measurements are "not too reliable" (Rossiter, 1977). Additionally, Rossiter (1977) has indicated that it is doubtful that children could comprehend 7-point "probable-improbable," "foolish-wise," etc., scales. If this is indeed the case, ranking scales may also be difficult to administer. Of course, alternative methods exist for the provision of direct similarity judgments, and a number of studies have compared their efficacy (Taylor, 1969; Taylor and Kinnear, 1971; Neidell, 1972). Yet, comparisons of alternatives typically have not involved children as respondents. It is this area of inquiry that concerns this study. [It should be noted that several studies have addressed the issue of measurement and children. For examples, see Calder (1975), Rossiter (1977), and Wells (1965); yet, none have addressed the issue of MDS and the efficacy of children's responses.]


Although numerous options exist for the provision of direct similarity judgments, this study will concentrate on the rotating anchor point (RAP) and magnitude estimation (ME) techniques. These approaches were selected because they vary in terms of scale orientation, task complexity, and their potential for data upgrading. As a result, the study seeks to operate in an exploratory sense to compare their efficacy. Basically, when dealing with children, there could be key differences between metric and nonmetric scale efficiency, not to mention differences between approaches in the levels of respondent fatigue.

With this in view, direct similarity judgments are to be obtained through the usage of each approach with the results serving as scaling inputs. MDS results will then be compared as to global fit, stimulus map convergence, and individual subject goodness-of-fit.

Basically, MDS comparisons, versus test-retest reliability measures, etc., should serve to enliven the study. In essence, scaling solutions permit one to assess the extent of recovery (via goodness-of-fit or variance re-suits) of a group's similarity judgments. If children are making random judgments, a limited two- or three-dimensional recovery would not be robust. However, if recoveries are high (i.e., low stress or high variance), common systematic judgments are in evidence. Further, if common systematics exist across alternative measurement approaches, the resulting spatial configurations may be compared as to convergence. If congruency exists, the validation can be suggestive of scale reliability. [It is noted that a comparison of approaches as to intransitivities (i.e., a lack of internal consistency in the data) was precluded because ME involves both conjoint and disjoint comparisons.]

Additionally, by making MDS comparisons, the results may contribute to a lessening of the dilemma of best choice (RAP or ME). In this regard, if MDS results are meaningful and consistent across techniques, one maybe advised to select the approach which is easier to administer. If the results are inconsistent, the approach which produces the better recovery may he more desirable. Of course, the results of this study will not be generalizable as differing stimulus sets both in nature and number of stimuli need to be evaluated. Yet, the results can serve as cursory insights into the efficacy of each technique.


Rotating Anchor Point (RAP)

This approach for attaining similarities judgments involves designating one brand, or stimulus object, as the anchor and then ranking the remaining brands as to similarity with the anchor brand. This means that the brand most similar to the anchor is ranked first, with the next most similar brand ranked second, etc. Of course, every brand serves its turn as the anchor, hence the term "rotating anchor point."

Since all of the rankings involve a stimulus in common (the anchor), the similarity judgments are viewed as conjoint. As a result, triangularization typically is used to infer the missing disjoint comparisons and to resolve those judgments which are intransitive (Taylor and Kinnear, 1971). The result is a complete (but not necessarily unique) order of pairs, hence more monotone constraints, for entry into the MDS program (Green and Rao, 1972).

Despite the upgrading feature applicable to RAP revealed similarity judgments, the approach is time consuming. For example, in the absence of group sorting, ten stimulus objects would require eighty individual comparisons, (n-1 C n)-n. Moreover, the larger the stimulus set, the greater the possible perception of task complexity and the greater the opportunity for fatigue.

Magnitude Estimation (ME)

This approach to the similarity judgment problem involves an evaluation of all possible pairs of stimulus objects, (n-1 C n)/2, along an assumed metric scale reflecting high similarity on one end and high dissimilarity on the other. [Although the term magnitude estimation is being applied to pairwise evaluations, one should recognize that it has also been applied to Stevens' (1957) ratio measures.] Assessments of similarity are indicated on the scale by having a respondent either circle a scale value or by showing relative similarity/dissimilarity on the scale itself.

The approach involves implicit judgments on both conjoint and disjoint comparisons but does not allow a check on the transitivity of the stimulus judgments (Taylor and Kinnear, 1971). However, the approach is characterized by lesser task complexity and a lesser opportunity for fatigue when contrasted to the RAP system. For example, a stimulus set of ten objects would necessitate only forty-five comparisons, or about half as many as the RAP approach would require.


It can now be easily determined that the selection of each of the alternative approaches for evaluation was prompted by their inherent trade-offs. In this regard, the RAP technique (plus data triangularization) offers nonmetric scales and data upgrading, yet its perceptual detail may subject the respondent to fatigue and a loss of interest. Alternatively, ME offers assumed metric scales and lesser perceptual detail and, therefore, in the latter case, a lesser opportunity for respondent fatigue and a loss of involvement. Still, ME foregoes data upgrading.



The necessary direct measures of brand similarity were obtained during May of 1978 by having seventy-seven children (fifth and sixth graders at the St. Francis School in Oldham County, Kentucky) provide similarity judgments on eight popular brands of cereals (see Table 1). This stimulus set was selected because it is basically familiar to children and because of its potential to interest children. To expedite the study, each cereal's package was briefly shown to the group.

In terms of sequence, children first utilized the RAP technique and, as a group, were able to complete their rankings in approximately twenty minutes. As one would expect, there was great variation in terms of individual respondent completion time. The ME technique required a group completion time of approximately seven minutes. [In this ME application, respondents were asked to show relative similarity/dissimilarity on the scale itself.] [The authors would liked to have alternated the sequence of technique presentation (e.g., one-half RAP and one-half ME) to preclude any order bias. However, technical constraints and class control precluded this effort. Still, given the rapidity of the ME technique, order bias did not appear to be too meaningful. Further, an analysis of individual respondent correlations between the original space and his/her private space enables one to make inferences as to fatigue or learning as a respondent moved from RAP to ME.]



The RAP judgments were triangularized through the usage of the TRICON computer program (Carmone, Green, and Robinson, 1968), and each data set (RAP and ME) was analyzed by the SINDSCAL program (Symmetric INdividual Difference SCALing) (Pruzansky, 1975). This program is an update of the earlier INDSCAL model (Carroll and Chang, 1969), only it is limited to symmetric data. Further, SINDSCAL was selected because of its optimal and unique orientation of the coordinate axes to the stimulus configuration and because of the insights it provides into individual respondent goodness-of-fit. [The falsity of SINDSCAL's data assumptions was tested through the application of the COSPA (Sch├Ěnemann, James, and Carter, 1978) computer program. The results for each data set strongly suggested that the common space and diagonality conditions for SINDSCAL were met (p < .001).]

Global Goodness-of-Fit

Scaling solutions were obtained on each data set in five, four, three, and two dimensions. A comparison of each approach as to the proportion of total variance accounted for by each dimensional solution (and a breakdown of individual dimensions) appears in Table 2. As can be seen, the data recoveries are fairly high. For example, the two-dimensional solution using the RAP technique accounts for 67.8% of the approximate explained variance, while the two-dimensional solution using the ME technique accounts for 69.3% of the variance. Further, the amount of total explained variance for each of the dimensional solutions is highly consistent for each of the approaches. A perusal of Table 2 also reveals that dimension one is given heavier weight in the ME procedure for the two-dimensional scaling solution.

Map Comparison

Since in each case there was only a marginal increase in variance in going from a two- to three-dimensional scaling solution, each two-dimensional configuration was selected for comparative stimulus map analysis. By assessing Figure 1 (derived from RAP input), one can see that dimension one (the horizontal axis) tends to denote sweetness. In this regard, cereals on the right side of the map are not as sweet as those on the left. Further, an assessment of dimension two (the vertical axis) suggests the usage of cereal shape as a perceptual cue. As can be noted, cereals toward the top of the map are all flakes, while those nearer the map middle have a puffier shape. Finally, those cereals toward the bottom of the map are all circular with a hole in the middle. [Such interpretations appear to be independent of cereal packaging characteristics (e.g., box sizes, colors, graphics, etc.). Given the briefness of the package presentations plus a poor visibility factor, package characteristics were not expected to impact upon perceptions. In essence, packages were shown merely to help generate an interest in the study.] A perusal of Figure 2 (derived from ME input) indicates a similar reflection of Figure 1. In essence, the same dimensional interpretations apply; hence, similar perceptual implications are in evidence. Also, an inter-point distance correlation of .99 is highly indicative of convergent validation. [Although a split-halves analysis was precluded, the fairly high degree of data recoveries and the presence of meaningful interpretations suggest that stimulus map convergence is a function of perceptual constructs. Basically, a map equalization due to a transferring of fatigue or loss of interest from RAP to ME appears remote. This is because fatigue or loss of interest implies a randomness of judgments.] This correlation was obtained from Carroll and Chang's (1969) INDSCAL model using their CANDECOMP option. In this application, Figure 1 and a reflection of Figure 2 were related to a group stimulus configuration.

Individual Subject Goodness-of-Fit

An analysis of individual subject goodness-of-fit can be made by viewing the correlations between the respondent's estimated private space and his/her original data. Of course, given the high level of global fit, individual goodness-of-fit would be expected to be high (an average correlation of .82 for the two-dimensional RAP and ME solutions, respectively). In fact, for the two-dimensional RAP solution there were only six respondents with correlations less than .6, while for the two-dimensional ME solution there were only four such subjects. Generally, the subjects with poorer correlations were not consistent across approaches. This may be due to the effects of learning, as some handled the second approach more efficiently; or it may be due to the effect of fatigue or loss of interest, as some handled the second approach less efficiently. At any rate, the simplistic character of the stimulus set and the nature of the correlations did not suggest the usage of idiosyncratic dimensional sets. Finally, a sign test as to directionality revealed no statistically significant difference between approaches.


Overall, the commonalties between the approaches, especially total explained variances and stimulus map similarities, suggest that magnitude estimation may be a viable approach for dealing with children's direct similarity judgments. Basically, it requires less workload and serves to lessen fatigue.

Of course, the results obtained in this study involved only eight stimulus objects. Likewise, the nature of the stimulus set may have facilitated the making of direct similarity judgments. As a result, a larger number of stimuli, more complex stimulus sets, and even younger children need to be evaluated. Still, in this example, nonmetric and assumed metric scales appeared to offer equal efficacy, and fatigue did not appear to be a major factor. Perhaps future studies which encompass varying children's age brackets may yield differing results. Such studies may also produce insights into the efficiency of MDS over more conventional approaches for the revelation of perceptual insights.








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