### Key driver analysis by combining mutual information and Pareto 80-20

In a recent conversation with one of our customers, the subject of managing overhead costs came up. In their business, nearly 90% of the costs comes from manufacturing overhead. However, these costs (and the percentage) are not fixed but fluctuate quite a bit. For them understanding the factors which influence this is pretty useful. In other words performing a key driver analysis for their costs can be highly valuable.There are many other cases where such key driver analyses can be helpful.

In this article we will demonstrate how to run a key driver analysis using mutual information and the Pareto 80-20 rule logic.

**What exactly is mutual information?**

Mutual information compares variables from a data set, two at a time to evaluate if they are mutually dependent or independent. (Wikipedia and other sources provide a more technical description of how mutual information can be calculated). It is somewhat similar in its objective to the chi-square test of independence, with a few differences. The **first difference** is that chi-square test is used to test nominal variables where as mutual information is used for numeric variables. The **second difference** is that chi-square test depends upon comparing the measured (observed) value of the ** chi-square statistic** to a standard benchmark (critical) value to make the assessment, whereas mutual information does not rely upon any benchmark. This brings us to the Pareto logic.

**How the Pareto 80-20 rule helps define an information "benchmark"**

As there are no predefined standards (or critical values of mutual information) to use as benchmarks, we must look for other ways to utilize the power of mutual information analysis. Applying the Pareto 80-20 rule is one way to do this, after we run a mutual information analysis between every pair of variables in a dataset.

First we calculate the total amount of information exchanged within the dataset by simply summing the mutual information reported for each pair. For example in a 4 variable dataset (let us call them A, B, C and D), each variable can be involved in 3 "relationships" and there will be a total of 6 unique relationships (AB, AC, AD, BC, BD and CD). A total amount of information exchanged can be measured by the sum of the mutual information exchanged between each pair. We can perform a standard Pareto 80-20 analysis as illustrated in the graphic below to rank the individual variables A to D. These articles provide more details on the generic 80-20 rule process.

A more sophisticated version of this process is used by the Basic Pareto option within KeyConnect, a web-app for performing key driver analysis. Try KeyConnect for FREE!

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