### Three calculations that benchmark analysts should use

This post is for the mathematically intrepid.

Present skewed data on log scales. My benchmark projects always lead me to think of normalizing data by company revenue: lawyers per billion, total legal spend per billion. From a recent article, however, I realize that perhaps it is possible to normalize data by the logarithm of the revenue (See my post of Jan. 14, 2007: explains log scales and log-log scales.). When data falls along a very wide range, notably revenue, you can cope by using log scales.

Subtract an industry average from a company’s figure. Since profitability (considered as return on equity) varies widely by industry, benchmark researchers can subtract from profitability of each company the average return on equity for all other firms in the same industry. This would turn lawyers per billion, for example, into comparable metrics across industries (See my post of Jan. 12, 2009: divide by the industry average.).

Present the coefficient of variation. When there is a normal distribution, such as amounts of invoices paid during a year by a large law department, the coefficient of variation is the standard deviation divided by the average. Between law departments or year-to-year for the same department, the coefficient of variation describes dispersion.

Check for multicollinearity. If an analysis uses multiple regression, such as to separate the effects of various drivers of litigation costs, it is very important to make sure that the predictor drivers (variables) are not themselves highly correlated. There are statistical techniques such as centering and likelihood ratio tests that can help spot such patterns.