Tendencies, proportions

From: Z net tutorials. Full list can be got here – Znet instructional’s

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:

1. The crime rate is higher in communities of color.

2.Therefore, whites are in greater danger from people of color than from other whites, statistically speaking.

3.Therefore, whites who discriminate against people of color in daily interactions are being rational.

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.
Survival Strategies

Huff gives five questions you can use to face a statistic and talk back:

1. Who says so? What might their agenda be? Do the authorities cited really say what is being claimed?

2. How do they know? What tests did they do?

3. What is missing? (Do they present significant results, sources of error, deviation, type of average, type of study they’ve done?

4. Did somebody change the subject? 5. Does it make sense?

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