Logical reasoning typically takes the following form:
1. I know that A is true.
2. I know that A implies B.
3. Therefore, I can conclude that B is true.
I, like Lewis Carroll, have problems with this process sometimes, but it’s pretty standard.
There is also a statistical version in which the above statements are replaced by averages (“A usually happens,” etc.).
But in all these stories, the argument can fall down if you get the facts wrong. Perhaps that’s one reason that statisticians can be obsessed with detail.
For example, David Brooks wrote the following, in a column called “Living with Mistakes”:
The historian Leslie Hannah identified the ten largest American companies in 1912. None of those companies ranked in the top 100 companies by 1990.
Huh? Could that really be? I googled “ten largest american companies 1912″ and found this, from Leslie Hannah:
No big deal: two still in the top 10 rather than zero in the top 100, but Brooks’s general point still holds. As Brooks said, we have to live with mistakes. This is more a comment on how a statistician such as myself will see a number and immediately feel the urge to check it.
If you don’t have that instinct—that feeling that numbers should directly correspond to reality—then I think you’re missing part of what it takes to really do statistics. A statistician who doesn’t care about the numbers can be helpful and even make major contributions, but I still think something is missing. The analogy might be a physicist who doesn’t like to tinker with machines or a chemist who doesn’t like to play around in the lab or a psychologist who has no curiosity about human motivations or an artist who doesn’t like to doodle.
Again, this is no criticism of Brooks—as a journalist, he’s of course more interested in good stories than in getting the details right (recall the notorious $20 dinner at Red Lobster). That’s ok. Storytelling is his job, numbers are mine.
P.S. There also might be some important part of the story that I’m missing. Brooks’s column doesn’t supply a link to his data source but I’m willing to be corrected if there’s something else going on.