| statsitical modelling (mds) | project index | statistical modelling (diagnostics) |
Introduction
mds (key terms | procedural topics) | research design issues (metric and nonmetric databases)What makes multidimensional scaling such a useful statistical technique is the transformation of nonmetric data into statistically useful metric data. This is achieved through the rank ordering of single elements, or the ordinal comparison of paired elements, of a stimulus set. How the stimulus set is defined is crucial to the results of the statistical experiment. There are many ways to compare both paired and unpaired stimuli. A few of them are listed below.
In order to compare well the elements of a set of objects, persons, or ideas one must have a clear idea about the standards utilized for comparison. This is not always possible when the elements of a set are complex or relatively new. Moreover, precise comparisons are not always desirable. In the first instance one may not know among a large number of standards which ones are the most important. In the second, an appropriate set of standards for comparison may not yet be available. In the third instance, one may only be looking for general impressions or gut reactions rather than carefully sorted statements of fact.
As researchers have the tendency to impose quantifiable relationships where none exists, they also tend to overestimate the strength of relationships between that which is perceived and how respondents express their perceptions. As imposing quantifiable relationships where none exists is a temptation often justified by statistical convenience, the researcher must be careful to eschew this desire.
Finally, researchers often puposefully select standards in order to achieve special ends not necessarily related to respondents' perceptions. By allowing respondents to employ their own standards of comparison researchers are likely not only to obtain more accurate data about the true perceptual space of the respondents, but they can also learn more about the standards that respondents use for comparison.Below are examples of several data collection techniques utilized by researchers to understand respondents' perceptions without imposing their own. One should be careful to note in this context that manipulation still takes place on the part of the researcher, insofar as he selects the elements for comparison.
top
- Conditional rank ordering
mds (key terms | procedural topics | paired order ranking | triad pair ranking
Consider the following seven urban centers: Hong Kong (HK), London (LD), New York (NY), Seoul (SL), Shanghai (SH), Singapore (SP), and Tokyo (TY). In order to learn how Hong Kongers identify with city dwellers of other major world cities respondents are provided with a list of cities with which Hong Kongers are likely to be familiar.The name of each city is presented in the column heading at the top of a table. There are as many columns and rows as there are city names. Respondents are asked to list each city according to its relative similarity with the city whose name appears at the top of the column.
A completed table might appear as follows:
Hong Kong
(HK)London (LD) New York
(NY)Seoul
(SL)Shanghai
(SH)Singapore
(SP)Tokyo
(TY)SP NY TY LD HK HK NY SH SH LD TY SP SH LD TY TY SH SH NY TY SL SL HK SP NY LD LD SH LD SP SL HK TK NY HK NY SL HK SP SL SL SP The obvious advantage of this method of data collection is that it encourages the respondent to use a variety of different criteria for comparison. Each column heading is likely to evoke a different set of standards by which the elements ranked beneath are compared. A Hong Konger who sees Hong Kong at the top of the list is likely to think differently than when he sees New York, Singapore, or Tokyo in the same place. As the standards he uses for comparison are his own, strong feelings about one city are likely to influence the way in which other cities are compared against it. Thus, the criteria employed for ranking may or may not be diverse.
top
- Paired order ranking
mds (key terms | procedural topics) | triad paired ranking
Pair ranking is another method for establishing rank order among data without imposing the researcher's standards of comparison. Paired order rankings are likely to involve more objective and diverse standards than those evoked by the conditional rank ordering provided above. This is because two cities are always viewed together.
Using the same number of cities as that employed in the previous example would yield 21 different paired combinations!7! / [2! (7-2)!] = 21 With so many pairs fatigue would set in quickly, and thus it may be difficult for respondents to provide very meaningful rank order responses. By reducing the number of cities to be compared by only two the number of pairs to be ranked can be cut by more than one half!
5! / [2! (5-2)!] = 10 A table of city-pairs for Hong Kong (HK), Singapore (SP), Shanghai (SH), Seoul (S), and Tokyo (TY) is provided below. Respondents are asked to rank each pair according to the degree of similarity of its elements. This time the standards for comparison are likely to be more uniform as respondents are compelled to assign a number to each pair based on his simultaneous cognition of all pairs. In short, he will look for standards by which all cities can be compared simultaneously.
Rank Paired city residents Rank Paired city residents 3 Hong Kong / Singapore 9 Singapore / Seoul 2 Hong Kong / Shanghai 8 Singapore / Tokyo 4 Hong Kong / Seoul 6 Shanghai / Seoul 5 Hong Kong / Tokyo 7 Shanghai / Tokyo 1 Singapore / Shanghai 10 Seoul / Tokyo Note: Presumably the pairs would be presented to the respondent in a random order, rather than in the more ordered presentation provided above for the purpose of illustration. top
- Triad pair ranking
mds (key terms | procedural topics)
Still another form of pair ranking might include the use of triads. This method is likely to result in more carefully considered comparisons than those evoked by paired order ranking, and be less conditioned than those provided with conditional order ranking.
If we used the same five cities (Hong Kong, Seoul, Shanghai, Singapore, and Tokyo), ten different triad-combinations are obtained5! / [3!(5-3)!] = 10 A table similar to the one below is then produced for each of the 10 possible triads. As the same pairs appear more than once among all ten triads, not only are the paired responses more carefully considered but the same pairs are judged more than once.
Most similar Least similar Hong Konger (HK) Singapore (SP) HK/SP HK/TK SP/TK HK/SP HK/TK SP/TK Tokyo (TK) top
- Rating scales
mds (key terms | procedural topics)
Still another data collection format might ask respondents to rate city pairs according to their degree of similarity. By comparing each city with every other city and rating each pair on a scale of similarity from zero to one hundred, a more quantitative picture with regard to each pair of cities is likely to be obtained. This method of paired comparisons is often used in conjunction with another form of rating based on the respondents own choice of criteria.
0 10 20 30 40 50 60 70 80 90 100 Hong Kong / Seoul X Hong Kong / Shanghai X Hong Kong / Singapore X Hong Kong / Tokyo X Seoul / Shanghai X Seoul / Singapore X Seoul / Tokyo X Shanghai / Singapore X Shangahi/ Tokyo X Singapore / Tokyo X
statsitical modelling (mds) top statistical modelling (diagnostics)