Re: What if 20 million illegals left?

Dennis (Icarus) wrote:

It's a representation of what the folks polled answer the questions.
You can guess that it extends out to how other folks would answer the
questions, but it's only a guess.

If the poll is conducted properly, and the results are analyzed correctly,
it's a "guess" whose accuracy can be mathematically determined to a high
probability. The "margin of error" that they talk about isn't a guess at
all.

Consider that you have a poll results, you think the questions are proper,
you think it's a relative sample.

"Representative" sample, not relative.

Now verify it.
How would you verify it to check the results?

You don't have to. Instead, you calculate the margin of error.
Interestingly, the margin depends only on the number of people polled and
on the results obtained, not on the size of the population whose opinions
you're intending to check.

If you're interested in how the math works, I can explain it, but for now
it's probably adequate to explain the thought process behind the math.

Basically, we recognize that a perfectly random selection of people will
almost never give us a 100% accurate view of the whole population. But
what we can do is calculate how likely our random sample is to be way off.
Assume for the sake of argument that if you *could* ask everyone, exactly
half of the people in the US want stricter gun control.

Now, what are the odds of randomly picking 1000 people who are all from the
anti-gun camp (assuming the random selection is really random)? Pretty
darned low, right? Well, we can calculate exactly *how* low.

How? Well, what are the odds that the first person we ask is anti-gun?
1/2. What about the odds that the first two are anti-gun? 1/2 * 1/2 =
1/4. All 1000? 1/(2^1000), which is infinitesimal.

That clearly isn't going to happen. Let's try another, more likely
scenario. What are the odds that we get exactly 600 anti's in our poll,
causing our poll to report 60% against guns, even though the "real" number
is 50%? Without getting into the math, it's also very small -- about
0.000000004%. The odds that we get exactly 500 anti's is about 2.5%.

We can pick a range and add all of these probabilities up. For example, the
probability that our poll will find between 470 and 530 anti's (assuming
the real ratio is 50% and the 1000 people are randomly selected) is 94.6%.
So, 95% of the time our poll of 1000 people will give us an answer of
between 47% and 53% -- and it's more likely to be closer to the middle of
that range than near the ends.

Of course, all of this has assumed that we know what the real percentage is,
but when we do a poll, we don't. So, what we have to do is to work the
same process backwards. The math gets trickier, but the thought process is
fundamentally the same -- and the math in question is extremely well
understood. So well understood that you can take those margins of error as
fact.

The other important assumption implicit in this is that the selection of the
people asked is *random*. If it's biased, then the whole thing goes out
the window, and biases can come from many sources. Maybe anti-gunners are
more likely to answer the question, while pro-gunners are too busy packing
up to head to the range and don't want to be bothered. Maybe the questions
themselves influence the answers, or the way in which they're asked. Maybe
the process of selecting the sample is subtly skewed somehow -- what if
only land lines are called, but, say, anti-gunners are more likely to use
only a cell phone and have no land line?

Actually, many of those biases can also be quantified, and there are ways of
mathematically removing their effect. This is where statistics becomes
something of a black art. Figuring out what factors to consider, and how
to estimate or compute their influence, is hard, and the process involves a
fair amount of subjective decisionmaking.

The established, reputable pollsters, however, have had very smart people
thinking very hard about these questions for decades, and they're really,
really good at what they do. It's very safe to assume that if Gallup says
that 51% of Americans favor stricter gun control, with a 3% margin of
error, then there's a 95% chance that the actual percentage of Americans
who favor gun control is between 48% and 54%, and it's probably towards the
center of that range.

Bottom line, from this pro-gun mathematician, is that if Gallup says a
slight majority of Americans say they favor stricter gun laws, it's highly
likely to be true, and almost certainly not more than 3-4% off the mark.

I suspect that most Americans haven't given the question enough thought to
have a very good opinion, which just makes clear that we need to do a
better job of educating our fellow citizens on the issues. In particular,
I think it's important to hammer on the facts that the portion of gun crime
committed by legal gun owners is miniscule, and that there is good evidence
that increased legal gun ownership reduces violent crime.

Shawn.
.

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