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Silent3

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Gender: Male
Hometown: New Hampshire
Home country: USA
Member since: Sun Oct 3, 2004, 03:16 PM
Number of posts: 10,060

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Understanding margins of error

I was listening to Lawrence O'Donnell earlier this week discussing some polls, and talking about what the polls said when you take into account their margins of error.

What he said was roughly correct, in a non-mathy sort of way, but also off enough to be a bit misleading.

First of all, margins of errors don't say anything about how good a polling model is, so it's not an expression of faith in the model. What the margin of error tells you is, if the model is good, how much would random variation in the particular people who get sampled typically throw off how well the model reflects reality.

Also, if a poll says, say, Biden is likely to get 52% of the vote, with a margin of error of 3%, that does NOT mean Biden is just as likely to get 49% as he is to get 52% -- it's a "bell shaped curve" -- and values near the middle are favored over values near the edges of the given range.



Margins of error are typically stated for a 95% confidence interval. So this example 523% will be in the range 49-55 95% of the time. 5% of the time the real result could even be higher or lower than that 3%. Only 2.5% of the time would Biden be at 49% or lower, Only 2.5% of the time would Biden be at 55% or higher. Typical results will cluster more towards the middle of the range.

Say that Trump is polling at 48% in the same poll. As O'Donnell explained it, he correctly pointed out that you have to apply the margin of error to both numbers, so even though 48% and 52% are 4% apart, the results overlap, with Trump possibly going as high as 51%, and Biden possibly going as low as 49%.

What O'Donnell got wrong, however, is speaking about this situation as if, "Hey, this essentially is a tie", since the margins of error overlap. Nope! This would still be a poll that looks much better for Biden than it does for Trump.

Without getting into the exact math, for Trump to actually be ahead in a poll like that requires that Trump pushes well into the more unlikely upper end of his range at the same time Biden happens to fall into the more unlikely lower end of his range. The sampling errors aren't very likely, however, to line up in just that way very often.

I had this thought of Trump viewing other people the way most of us view vending machines

This is just a bit of very amateur psychological speculation, so take it for what it's worth.

It's a given that Trump is a narcissist, and almost certainly a psychopath too. He's completely transactional in his behaviors, and people only have value to Trump insofar as they provide for Trump's needs.

So I'm imagining people to Trump as vending machines, and the words he says -- be they true or false -- are the coins he drops into these vending machines, and the buttons he pushes.

Particular coins and particular buttons are supposed to result in particular items being dispensed. "Truth" isn't a consideration, nor is consistency. If something doesn't work, try something else.

Saying "I will protect Social Security, and Biden will destroy it" is the input that's supposed to produce senior votes for Trump as an output. "I'm the least racist person in the room, and Biden backed that terrible crime bill" is the input that is supposed to produce more black votes, or at least more white votes from white people who want to believe they aren't racists.

And just like you or I might get annoyed or angry when a machine eats our coins, but doesn't drop the candy bar we wanted, or the bag of chips gets stuck behind the glass, or the cup lands upside down and our drink pours around it and down the drain, Trump is genuinely angry when his words and gestures don't produce the results he wants.

It's not our job to worry or care about the truth or consistency of what Trump says. As far as he sees it, he's saying what he's supposed to say for us to do what we're supposed to do for him. If we don't respond correctly, he'll get angry, he'll shake us, he'll pound on us, he'll kick us, and he'll wonder out loud what's the matter with us.

If we don't "work", we're useless junk.
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