Sunday, September 15, 2013

Matrix Data Analysis Chart (MDAC): How to understand it

How to understand it
When comparing a large set of items, the complexity of the situation can make it difficult to determine how different factors relate to one another. In particular, it can be useful to find groups of items that behave in similar ways. For example, a washing powder may have different efficiencies at achieving 'softness' and 'stain removal' in garments made of acrylic, polyester, wool and various fiber mixtures. If similar affects are found in a group of fibers, then changing the powder ingredients may affect the whole group in a similar way.
The Matrix Data Analysis Chart (or MDAC) helps classify items by identifying two major characteristics common to all items and then plotting each item as a point on a standard x-y chart. This makes it easier to see how the individual items relate both to the characteristics and to one another, thus:

Fig. 1. MDAC plot
Identifying the best characteristics to measure is an important task, as different sets of measurements can give very different charts. It would be useful to be able to compare many characteristics together, such as the density, color, texture, strength, etc. of cement mixtures, but we are constrained by the two dimensions available on paper. There are mathematical methods for combining multiple factors, but these are beyond the scope of this book.
A key interpretation point about an MDAC is to consider how points on the chart group together or form into clusters (this may be contrasted with the Scatter Diagram, which looks for lineartrends). This interpretation is helped by highlighting significant groups of points with linear links, as in Fig. 2.

Fig. 1. Clustering
Typical items of interest on an MDAC include:
The behavior of logical groups of items, which might be expected to form close clusters. For example, in a washing powder test, logical groups might be woolen items, acrylics and mixtures.
Actual clustering on the chart which might highlight divergence from expected behavior, and prompt new actions. For example, investigation of an unexpected cluster of different fiber types might show that they come from one manufacturer who has developed processes to give different fibers with similar specifications.

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