The importance of back-of-envelope calculations

In my personal and professional work I often use what I call back-of-envelope calculations. By this, I simply mean rough calculations intended to test analysis and assumptions.

To use  a private sector example, say you have a business plan. Then you take the assumptions involved and just do some rough calculations as to what happens if those assumptions are varied in some way. This will quickly show you what the problems might be.

Or take a Government policy move and look at  Back of envelope calculations - is the purchase of Toorale Station a waste of money? as an example. There is nothing magic here, just rough tests.

I mention this now because I have just finished New England demography 2 - problems with projections. This is a pure regional post, not something that would be of interest to a broader audience. However, it illustrates my point.

The NSW Government has released population projections for NSW through to 2036. These are the numbers on which key planning decisions will be based. They include an entity called "Northern." This is basically the Northern Tableland and Western Slopes. The projections suggest that the population of this entity will decline from  180,000 in 2006 to 168,000 in 2036, down 12%.

When I read this I thought that it was odd. I also noted that mayors from the area were attacking the number. Well, it is odd and the mayors are right.

Frankly, and I stand to be corrected, the simple test I have done suggests that the projection is absurd. I have put this strongly, but I can think of no other way to describe it.

I am sure that the projection is based on solid statistical techniques. Yet all such results need to be tested because they are based on assumptions. In this case, the simplest test suggests that the results are silly.

Does this matter?  

Certainly it matters if your are from "Northern" because you are going to get few resources. How can you justify investment of any type if population is falling? However, there is a broader point.

In a measurement dominated world, if you want to bring about change or achieve improvement, you must test the validity of the measures on which decisions are based. Frequently, you will find that the measures are wrong.