# Multi-Dimensional Scaling

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## Multi-Dimensional Scaling

Multi-dimensional scaling (MDS) is a statistical technique that allows researchers to find and explore underlying themes, or dimensions, in order to explain similarities or dissimilarities (i.e. distances) between investigated datasets. You can analyse any kind of similarity or dissimilarity matrix using multi-dimensional scaling. Plotting these data sets on a multi-dimensional scale allows for easier interpretation and comparison by researchers than a linear dataset permits.

A possible example of when multi-dimensional scaling (MDS) might be used is if we have six utility companies and we want to understand how they are considered differently by respondents. We would invite consumers to complete a survey in which each of the six companies would be paired with each of the others, and the respondents would be asked in a series of scale based questions how similar they believe them to be, for a number of attributes. Examples of attributes may be: quality, service and price.

We can specify that we would like to reproduce the data on two dimensions. As a result of the MDS analysis we would get an output for each attribute rated that shows the two dimensional representation of how similar or different the companies are viewed. This makes the data much easier to look at and gives the observer a clearer sense of how different each company is. This can be used in brand positioning, identifying if work is needed to make a particular utility company’s brand more unique in the specific market place.

In market research, multi-dimensional scaling is often used to plot data such as the perception of products or brands; this will display both the number and nature of the dataset in an easy to interpret, visual way. This being said, any kind of data with meaningful similarities or distances can be displayed using multi-dimensional scaling. Classical multi-dimensional scaling portrays similarities and dissimilarities between pairs of items on a coordinate matrix.

Interpreting the dimensions is made simple by plotting them in a two dimensional coordinate matrix (scatter graph); three dimensional data can also be displayed graphically but is more complex to read. Once plotted, researchers can better explore the data and any patterns or clusters occurring. Plotting more than two or three dimensions is possible, but it is understood that with each additional dimension, the output matrix becomes more difficult to interpret.

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