Tuesday, November 22, 2005

More on two types of numbers

A few months back, I posted on two types of numbers. I just saw an example that shows how the distinction can be important in communicating ideas.

In a story including material from Washington State's Chief economist, Chang Mook Sohn, my local paper wrote, "The housing bubble hasn't popped yet, but a cool-down probably is imminent, Sohn said. National housing starts dropped 5.6 percentage points in October, he noted. 'There are many signs that housing is peaking.'"

I don't mean to be picking on Sohn; you can find other examples easily, I suspect. His comment just triggered my thoughts. What did he mean by "housing is peaking"? If he was referring to the stock of houses, then "peaking" might imply that the number of houses would decline significantly (if it weren't significant, why would he mention it?). That doesn't seem quite likely; are there other alternatives?

Perhaps he was referring to the average price of houses. That's a stock, too. Perhaps he thinks prices will decline, maybe even significantly; the article did use the word "bubble." That could be a bit scary for a homeowner.

The article also mentioned that "housing starts dropped 5.6 percentage points." Perhaps he's referring to a peaking in the rate at which housing prices rise each year—something related to a flow into the average selling price. That's not nearly as scary. Sure, homeowners may not get the high on-paper appreciation they're used to seeing, but a leveling off of prices with no decline sounds like part of normal life. Those prices could follow the path of an S-shaped curve.

What's the lesson for those of us trying to relate such information? I think there are three.

  1. Make it as clear as we can whether we're speaking of a stock or a flow. A peaking in a flow may not be nearly as scary as a peaking in a stock. Changing a flow may not be nearly as impressive as the eventual resulting change in the associated stock.
  2. Use a graph whenever we can to help clarify what we mean. While not impossible, it is hard to communicate the essence of change over time in words.
  3. Show a general preference for words reasonably low on the ladder of abstraction. We learn powerful abstractions in school to help us move to a higher level of thinking, but, without the discipline of a common textbook or professor to set definitions carefully, we can mislead if we and our readers mean different things by the same high-level term.



Blogger Bill Harris said...

Did I really say that? I guess I did. I'd like to modify Lesson 2 above just a bit: numbers work well, too, in many cases, although there's nothing like a graph to show a variable over time. Check out Tufte's The Visual Display of Quantitative Information for places where tables of numbers might serve us better.

23 February, 2007 14:35  

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