Seeing History
Statistics

Numbers count. But only if you know how to read them. "Statistics" has two senses: (1) a collection of numerical information about something, and (2) techniques of analyzing situations due, or not due, to chance. Here is an example of statistics in the first sense.

Britain lives by imports; it breathes through external lungs. In May 1943 (a global war then being in progress), a total of 199,409 gross tons of Allied shipping destined for Britain were lost to German submarines. At first glance, thinking of all that food lost and all those sailors drowned, we can only exclaim: That is simply awful. More coldly, we may ask: Hey, compared to what? To those who were in charge of the war, was that number good news or bad news? To find out, we glance up the chart to April 1943, when the loss was 241,687 tons, and to March, when it was 514,744 tons. So in context, the May figure was not only good news, it was decisively good news. It marked the defeat of the only effort by which Germany could have won World War Two. That mid-ocean result meant that England would live, and that the later Allied effort on the Continent would in fact be made. It meant that Hitler was doomed.

Month 1943	Tons Sunk
March	514,744
April	241,687
May	199,409
June	21,269

Both Churchill (Prime Minister on the British side) and Dönitz (Chief Admiral on the German side) were studying this list of numbers. Intently. Can any student of their war afford not to do likewise? The secret here, as in many another case, lies not in any one number, but in the trend of the numbers taken together.

In June 1943, the figure dropped to 21,759 tons. The Americans were building ships faster than the Germans could sink them, and the British (with a little help from Alan Turing) were sinking submarines faster than the Germans could replace them. Dönitz pulled his submarines back, waiting for a German technological edge to develop. That technological edge did appear. It appeared in April 1945. It was too late. The war was not over, but the outcome of the war was no longer in doubt.

So you see, it was easy to interpret that number. But easy stuff like this is only the surface of the ocean. There are also numbers which tell the desired story, but which are more difficult to read at sight. For them, some analysis is necessary. The cover name for the set of analytical techniques which are relevant to such situations is "statistics" in sense (2), above. Statistics in this sense was the joint invention of Newton's friend Abraham de Moivre in England, and Jacob Bernoulli in Switzerland, and all that followed from their fundamental work. Here is Bernoulli:

Among the kinds of questions which statistics (2) can answer are:

• How likely is it that this could have occurred by chance?
• Are these concepts associated in the mind of Mencius?
• Did Spring and Autumn diplomacy have any effect on Spring and Autumn war?
• Is Colossians in the style of the Apostle Paul?
• Is there an overall trend in these trade reports?
• If the usual level in this river is 3 coliform bacteria per liter, and I get a sample with 5, are we in trouble?
  • [Not to be too tantalizing, the technique for answering this question may be found here]
• Were Colonial American landowners more conservative than other citizens?
• How many hypotheses are there about the authorship of the Jwangdz?
  • [This one is merely hilarious, but as a reminder to avoid being hilarious to the rest of the world, click here)
• Of these two simultaneous factors, which more strongly affects the outcome?

The historian who can answer these and other questions, rapidly, routinely, and with confidence, is in a much stronger position than the one who cannot. It follows that departments of history should require familiarity with these techniques, right up there with the Latin Fourth Declension. This happens not to be the case at present. So as things now stand, those wishing to be competent at the countable part of history will have to pick up their competence in the gutter. Too bad, but at least we know where the gutter is.

As a gesture to gutter learning, we will now illustrate just one statistical technique, and give a hint about its application to practical situations:

17 Dec 2006 / Contact The Project / Exit to Outline Index Page