# Thread: Comparability and Large Number Theory

1. ## Comparability and Large Number Theory

I wish to assess the usual profit made by a company in a country. This is for transfer pricing purposes - I need to know what the 'market rate' profit on sales is, so I can set inter-company transactions at a level which gives my subsidiary company the same 'market rate' return on sales.

"How Not To Be Wrong" (Jordan Ellenberg) has re-introduced me to large number theory. And raised an interesting question.

The smaller the sample size, the more similar my company is to the companies with which I am comparing it (they are operating in a more similar market).
However, the smaller the sample size the more variability is inherent in that sample size.

How do I assess when the differences between my company and the ones I am comparing it to are less than the inherent variability due to the sample size?

How do I balance these two competing drivers?

2. ## Re: Comparability and Large Number Theory

As a problem in pure math, this belongs under Statistics or Advanced Statistics, and I am not competent to discuss the math aspects.

However, I doubt that this is a pure math problem at all. The number of companies that have similar lines of business and for which you can get reliable comparables is likely to be quite small. So the resulting estimate is going to be fairly crude in any case. If I were doing this, I'd go ahead and ask the statistics folks this question, but recognize that the resulting answer has a high probability of being impractical to apply. So I would concentrate on making sure that the members of the sample are in fact highly similar to your company. Transfer pricing is nowhere close to being an exact science.