What Is Multidimensional Scaling?

Multidimensional scaling is a method used to create comparisons between things that are difficult to compare. The end result of this process is generally a two-dimensional chart that shows a level of similarity between various items, all relative to one another. For example, a researcher may give test subjects several varieties of apple and have them make comparisons on several criteria between two apples at a time. Once all the apples are directly compared to each other variety, the data is plotted on a graph that shows how similar one type is to another.

The two components of multidimensional scaling are right in the name, multidimensional testing and scaled response. Both of these concepts are very simple — it is just the analysis at the end that makes this process complex. Multidimensional testing simply means that many factors of the test item are examined at the same time. In the apple example, things such as color, level of sweetness or tartness or even how firm the fruit is may be discussed.

Scaled response of multidimensional scaling refers to the method used to compare the factors. This is generally a five- or seven-point scale that ranges from not alike at all to identical. This allows the test subjects to interpret the questions and give answers based on their feelings rather and concerning themselves with right and wrong. This also has the added benefit of creating a numerical result, one through five or seven, which researchers may use to mathematically manipulate the data.

These sorts of studies have both a minimum and maximum for comparison. If there are too few comparisons or compared items, the data may show artificial similarities where none are present. When there are too many, the comparison systems become so overloaded with information that the result is typically inconclusive. Generally, between four and eight comparisons are made between four and 12 items.

In a multidimensional scaling experiment, the subjects look at two items at a time. They make comparisons between these items alone, not considering any other stage of the test. Eventually, the subjects will compare every item against every other item, all in groups of two. For instance, the comparison may be between the sweetness of apple one and apple two. The similarity between the sweetness of the two fruits is assessed on the point scale and the subject moves on to the next question.

After the data is collected, a program that assesses the multidimensional scaling experiment’s results performs a complex statistical analysis on the information. First, the comparisons on similar factors, such as color, are compared to one another in absence of all others. Then the comparisons of a single item are compared, in the absence of all others, and both are weighted. These results are then aggregated into a final tally that shows a numerical similarity between multiple dissimilar objects.