Tuesday, March 28, 2006
Statistics and Stereotypes
Anyway, if I can ever solve this one (or steal a solution from my faithful readers, hint, hint...), I might actually get through to a cluster of students I’ve never really reached. Oh, faithful blogsophere, I ask your assistance...
In the extended triple overtime after the 2000 election, a student asked me why the red/blue map was so red, if the election was so close. I considered that a great question, and responded that one reason was that Democrats are likelier to live in cities, so a lot of votes are crammed into a small space. She asked why Democrats are likelier to live in cities. I responded that one reason was that party affiliation often correlates with race, and so areas with high concentrations of African-Americans could be expected to vote Democratic, and that usually means cities. The exchange after that:
Student: So you’re saying black people are Democrats?
DD: No, but the Democrats usually win 80 to 90 percent of the black vote. So if a city is mostly black, you could be pretty confident that it would vote Democratic.
Student: That’s not true. I think it’s up to the individual.
I’ve had variations on this conversation many times, and that student response always brings me up short.
Is there a reliable way to prevent this apparent confusion of description and prescription? Is it that they don’t understand what percentages mean? I’m perplexed. I think the student is trying to be morally virtuous and reject stereotyping, which prevents her from actually trying to understand what I’m saying. Once the student decides that you’re evil, of course, no amount of explanation is going to work. Is there a way to describe demographics without triggering a defensive anti-stereotyping response in students?
I usually talk about correlation versus causation. But maybe this just confuses things further.
In my last comment I also pointed out that we don't weight votes by how big a yard is, we weight them by person. So, if on average those who vote blue (minorities in many cases) have smaller yards concentrated in cities, then a small proportion of a map will be blue.
The problem is one of understanding probability. I also have trouble communicating logical possibility vs. probability.
If you take the perspective of an individual voter, the role of party identification may not loom that large. That might even be right. For example, even in your 80/20 case, how confident would you be to identify *who* would vote against the tide? If you could bet your retirement on the vote of a single voter with those odds (say you get 9 times whatever you've saved up if you're right), would you?
Getting people to take the sample/statistical perspective is a really important cognitive shift and one that doesn't come naturally.
And that's not always wrong. Right now I'm listening to an audiobook about the fall of Long Term Capital Management and the hubris of these economists is just profoundly stunnind got me.
And, of course, those predictions will change with time, if enough individuals make individual decisions that change the math. That's what keeps actuaries employed. (It used to be that most Southern blacks voted Republican, after all.)
I do find it is written in layman's terms, the causality/correlation is also explained to some degree. Maybe they enjoy it.
A student can see this by looking at a "population cartogram," a map with the states redrawn so that a state's size is proportional to its population. Such a map can be found on http://www-personal.umich.edu/~mejn/election/, the third map down.
In our family we have an instinctive understanding of math and it annoyed us that people were fooled by the 2000 election red/blue map into thinking that Bush won a large majority of votes, when actually he lost the popular vote. We referred to the red/blue map as the Cow Vote Map, because the states are scaled more closely to their cattle population than their voter population.
-- Cardinal Fang
So I think it's safe to say that yes, black people are Democrats.
-- Cardinal Fang
First, my guess is that the student is bothered by the apparent causal relationship in your explanation. I know I'm simplifying this, but they might think you're saying that someone will vote Democratic because they're African American.
They might be looking at your explaination in the same way that you would look at statement like this:
Everyone dies after eating peanuts.
While, technically that statement is true, (eventually, we all do, right?), it just doesn't sit well because the two actions, eating peanuts and dying aren't necessarily related (at least not for everyone).
So, the point that I'm coming to here is that there are probably multiple characteristics of cities that correlate with voting patterns and it's hard to know which characteristics caused the observation.
For example, people in cities tend, on the whole, to be more highly educated than people in rural areas. And, there is a strong correlation between education and voting patterns. Needless to say, the more education you have, the more likely you are to vote Democratic.
It seems we keep forgetting a couple key points.
1. This has nothing to do with sampling. The election is a measure of the total population (the only population that matters is the population of votes.) There is no sampling error introduced in elections, no deviation frome the mean--none of that. Remember, statistics is designed to help us infer something about the population when we cannot actually measure the whole population.
2. The typical maps were so largely red because a) in 2000 they didn't do shading, thus a 50%+1 vote margin for one candidate would receive that candidate's color--period. b) Many of the maps were developed that way based on the electoral college vote-again, not a shaded measure, but an all one color measure.
3. Sampling only comes into play when we seek to understand the correlation between numbers of a population that have a given race, and their political affiliation. This is usually done by asking a series of questions, in a poll, and then looking at the paired data "From Venus, Green Party" for instance. Yes, the data then reaches some "conclusions" and must be shared with some understanding of the sampling error, and sampling methodology, and the like--but these sorts of things are designed to identify trends, not individual behavior.
4. No one likes to have discussions that seem to imply prejudging of individuals, and saying that someone is "____" (race) and thus highly likely to be "_____"(party) leads one to assume that when engaging that person. And while we all want to think we are free of prejudging, we all do it. The blog "Targuman: Inside Higher Ed :: The Real Bias in the Classroom" references an article where students pre-judge professors based on what they THINK a professor's views are, rather than judging each individual.
For instance, based on this discussion, I of course would continue to say that not all academics are liberals, but those that commented here generally seem to be (and perhaps even are somewhat prejudging of people who come from rural areas (refered to in a pejorative as "boonies" by the way...) and thus assuming they voted for Bush.
Bottom Line: Tell your students to please treat each person you meet as an individual, and make few assumptions about them before getting to know them. But tell them to understand that in the aggregate certain views are "dominant."