Tendencies,
Proportions
The reason we have to talk statistically at
all is because the definite assertions that are needed for logic are never
true. If all we had in our toolkit was logic, we couldn't make a statement like
"Women earn less than men". We could say "all women earn less
than all men", which wouldn't be true, or say "some women",
which would be true but from which we couldn't come to many conclusions. So we
use statistics and talk about 'tendencies', 'proportions', 'disproportionate
numbers', and so on. Are these concepts meaningful? Are the conclusions drawn
from them meaningful? Well, sometimes yes and sometimes no. Let's see.
Tendencies are related to averages. In the example above, we
could accurately say that (a) "women tend to earn less than men".
This means that on average, women make less money. Is there anything that
follows immediately from this? We are talking about tendencies so our
conclusions will be about tendencies as well. So we could pretty safely make
the conclusion "women will tend to have less money to spend than
men".
What about "Sarah will tend to earn
less than Joe?" Can we conclude that from (a)?
Well, no. Sarah can't tend, one way or
another. Sarah's an individual, so is Joe. She can be compared to the tendency
("Sarah earns more than average") but she can't have a tendency of
her own, in the statistical sense.
Can we draw any conclusions about
individuals, from tendencies?
In the logical sense, no.
We can make guesses, and that's what
statistics is about. Making the best guess.
But isn't this a slippery slope towards
'rational discrimination'?
Rational discrimination is the right wing
idea whose logical form is as follows:
This is a racist argument,
and entering into it at all is a dehumanizing exercise. It could be done on
many different grounds, especially the factual and the moral. But since we're
here to talk statistics, let's look specifically at premise (2), which is
inferred from premise (1). Does it follow from (1)?
No.
Well, when you hear
something like "the crime rate is higher in communities of color",
you have to begin asking a lot of questions. Is the crime rate the number of
crimes committed by people of color divided by the number of people of color?
Is it the number of crimes committed by people of color divided by the total
population? Does it contain any information on the number of victims?
The "crime
rate", traditionally, means the number of crimes divided by population. So
if you're not interested in crimes against all people, but only against whites,
as racists are, then you shouldn't look at the crime rate in communities of
color. You should look at the number of crimes against whites committed by
whites, and compare that to the number of crimes committed against whites by
people of color.
Unfortunately for
the racists, most white victims of crime are victimized by other whites. Most
crime happens between people who know one another and in a segregated country,
most whites are in social circles with other whites, and the same goes for
people of color. Statistically speaking, then, whites should discriminate
against each other.
This demonstrates
that the entire argument is a misapplication of statistics, and proof that skepticism
is warranted when any conclusions are come to about individuals by averages
about populations.