Thursday, April 28, 2005

Careful writing <=> careful thinking

Reading an Associated Press article in Monday's local paper about the growing inmate population in the United States reminded me how confusing what we write and say can be.

People in the field called system dynamics speak of two fundamentally different types of numbers.


  • Levels (or stocks) correspond to what we sometimes think of as accounts, such as our bank accounts. They represent things we can count or measure, even if we could freeze the world and stop all motion (except for us going around and counting or measuring, of course).
  • Rates (or flows) correspond to changes per unit time in a stock. If you could freeze the world, stopping everything from moving, then all the rates would go to zero. For example, if a stock is the amount of money in our bank account, a corresponding flow might be the money flowing out of that account: our expenses per month (or per week or per day). Rates always have an explicit or implicit "per unit time" appended to their name: profit earned per year, tons shipped per week, etc.


Why should we care?


  • You can't compare a rate and a level as if they were equivalent. If Acme Bakery has $1M in revenue per year (a rate), while Better Breads has $2M in cash assets (a level), you can't automatically say Better Breads is twice as wealthy as Acme Bakery.
  • Rates usually change more quickly than levels.
  • We don't directly change levels; we change the rates to affect their associated levels.


The AP article tended to confound those terms. It led with "Growing at a rate of about 900 inmates each week between mid-2003 and mid-2004," which is a good use of a net rate in the system dynamics sense and not confusing at all. Later, it said "the number of people in prison and jail is outpacing the number of inmates released," seemingly a comparison of a level (the number of incarcerated people) and a rate (the number released per unit time, presumably). Hmm. Maybe what they meant is that the number of people entering prison and jail (a rate) is larger than the number leaving (another rate), which would drive up the number of incarcerated people (the level).

Sometimes people refer to a "rate" when they mean a percentage, fraction, or ratio. For example, the sidebar (not available online) said that the "rate of people incarcerated in the U.S. has steadily increased since 2000." Table I of the original U.S. Bureau of Justice Statistics report indicates that they indeed are speaking of a ratio (the number behind bars per 100,000 residents), not a rate in the sense I'm talking about here. If you read it quickly, you might not know whether the numbers in the sidebar represented a rate or a ratio.

I invite you to be careful when you read, think about, or write such reports. Distinguish in your own mind which numbers are levels, which are rates, and which may be ratios. If you're writing the report, think about how to communicate that distinction well to your readers so they can make good decisions, too.

We'll talk more later.

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