The Language of Argument

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Statistical Generalizations

STATISTICAL GENERALIZATIONS

One classic example of an inductive argument is an opinion poll. Suppose a

candidate wants to know how popular she is with voters. Because it would

be practically impossible to survey all voters, she takes a sample of voting

opinion and then infers that the opinions of those sampled indicate the over-

all opinion of voters. Thus, if 60 percent of the voters sampled say that they

will vote for her, she concludes that she will get around 60 percent of the vote

in the actual election. As we shall see later, inferences of this kind often go

wrong, even when made by experts, but the general pattern of this reason-

ing is quite clear: Statistical features of a sample are used to make statistical

claims about the population as a whole.

Basically the same form of reasoning can be used to reach a universal con-

clusion. An example is the inductive inference discussed at the start of this

chapter: All observed ravens are black, so all ravens are black. Again, we

sample part of a population to draw a conclusion about the whole. Argu-

ments of this form, whether the conclusion is universal or partial (as when it

cites a particular percentage), are called statistical generalizations.

How do we assess such inferences? To begin to answer this question, we

can consider a simple example of a statistical generalization. On various

occasions, Harold has tried to use Canadian quarters in American vending

machines and found that they have not worked. From this he draws the

1. The sun is coming out, so the rain will probably stop soon.


2. It’s going to rain tomorrow, so it will either rain or be clear tomorrow.


3. No woman has ever been elected president. Therefore, no woman will
   ever be elected president.


4. Diet cola never keeps me awake at night. I know because I drank it just
   last night without any problems.


5. The house is a mess, so Jeff must be home from college.


6. If Harold were innocent, he would not go into hiding. Since he is hiding,
   he must not be innocent.


7. Nobody in Paris seems to understand me, so either my French is rotten or
   Parisians are unfriendly.


8. Because both of our yards are near rivers in Tennessee, and my yard has
   lots of mosquitoes, there must also be lots of mosquitoes in your yard.


9. Most likely, her new husband speaks English with an accent, because he
   comes from Germany, and most Germans speak English with an accent.


10. There is no even number smaller than two, so one is not an even number.

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