Erik Henry
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On Bill O'Reilly's web page there was a link titled "Don't Believe the NYT Poll" that linked to this story criticizing a NYT poll showing support for union workers.

Here's the relevant quote from "A Shoddy New York Times Poll":

Quote:
Although less than 12 percent of the workforce is unionized today, 20 percent of the households in the survey had a union member. Although government workers are 17 percent of the workforce, 25 percent of the households surveyed had one living there. In other words, the sample was wildly skewed toward the very people most likely to give the answers the Times was hoping to hear.

They had me sold for a couple of seconds. And then I realized they were comparing the amount of union members (or government workers) with the amount of households that included them. Let's assume for a moment that most households have two adults and that union members and government workers are randomly distributed across the population. Then, if 12% of the workforce is unionized, you'd actually expect that 23% of households would have a union member [1-(1-0.12)*(1-0.12)]. Likewise, if 17% of the workforce is government workers, then you'd expect 31% of households to contain a government worker [1-(1-0.17)*(1-0.17)]. So based on those assumptions, the survey actually undersampled union and government-worker households.

In reality, however, the average adults per household is probably a little less than two, and there is probably some clustering of union/government workers in households above the rate you'd get from a random distribution. Still, though, based on the quoted data I don't see how they can come to the conclusion that the "sample was wildly skewed."
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Erik Henry
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Women only make up 50% of the population, and yet almost 90% of households surveyed had a woman in them! How can that be a random sample!
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Ben Foy
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Erik17 wrote:
They had me sold for a couple of seconds. And then I realized they were comparing the amount of union members (or government workers) with the amount of households that included them. Let's assume for a moment that most households have two adults and that union members and government workers are randomly distributed across the population. Then, if 12% of the workforce is unionized, you'd actually expect that 23% of households would have a union member [1-(1-0.12)*(1-0.12)]. Likewise, if 17% of the workforce is government workers, then you'd expect 31% of households to contain a government worker [1-(1-0.17)*(1-0.17)]. So based on those assumptions, the survey actually undersampled union and government-worker households.


You are right about the flaws in Bill O'Reilly's argument but your math is also flawed. You forgot to account for the households that have 2 (or more) union members or government employees.
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Erik Henry
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BFoy wrote:
Erik17 wrote:
They had me sold for a couple of seconds. And then I realized they were comparing the amount of union members (or government workers) with the amount of households that included them. Let's assume for a moment that most households have two adults and that union members and government workers are randomly distributed across the population. Then, if 12% of the workforce is unionized, you'd actually expect that 23% of households would have a union member [1-(1-0.12)*(1-0.12)]. Likewise, if 17% of the workforce is government workers, then you'd expect 31% of households to contain a government worker [1-(1-0.17)*(1-0.17)]. So based on those assumptions, the survey actually undersampled union and government-worker households.


You are right about the flaws in Bill O'Reilly's argument but your math is also flawed. You forgot to account for the households that have 2 (or more) union members or government employees.

No, my math accounts for that . . . . as long as the workers are randomly distributed. What it doesn't account for, as I mention above, is the extent to which those workers are non-randomly clustered. For example, one might expect union workers to largely occupy a similar social stratum, and so a union member might be more likely to marry another union worker versus a random person from the overall population. That clustering would drive the expected "percent of households" number down.

To properly draw a conclusion I'd think you'd need some statistics on that clustering (and the number of workers per household).
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Chad Ellis
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I'm sure O'Reilly will issue a prompt retraction and apology. He really cares about integrity. Just ask him.
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Chad Ellis
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The article isn't just bad at math -- it's bad at basic reasoning.

Quote:
“Asked how they would choose to reduce their state’s deficits,” the Times adds, ”those polled preferred tax increases over benefit cuts for state workers by nearly two to one.”

How do you square these figures with the results of last November’s elections, in which anti-tax, anti-deficit, anti-public-union forces swept to historic victories in federal and state elections across the country? Well, you can’t, of course. The Times doesn’t even ask this blindingly obvious question, let alone try to answer it.


So just to be clear...according to the author, it's literally impossible for the minority party to make huge gains during the middle of a huge recession unless the nation agrees with them on pretty much every issue? That is, you can't square a preference for tax increases vs. state worker benefit cuts with the November elections.
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Ben Foy
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Erik17 wrote:
No, my math accounts for that . . . .


You are right. You did the intersection of the opposite of the event, instead of the more straight forward union of the events minus the intersection. I don't deal with this stuff enough so I'm losing it.

Erik17 wrote:
as long as the workers are randomly distributed.


Well you'd need to know what percent of households have one worker, what percent have 2, what percent have 3, etc... to get the probability of a household having a government employee (or union member).

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Erik Henry
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BFoy wrote:
Erik17 wrote:
No, my math accounts for that . . . .


You are right. You did the intersection of the opposite of the event, instead of the more straight forward union of the events minus the intersection. I don't deal with this stuff enough so I'm losing it.

Erik17 wrote:
as long as the workers are randomly distributed.


Well you'd need to know what percent of households have one worker, what percent have 2, what percent have 3, etc... to get the probability of a household having a government employee (or union member).


Yeah, I agree. And if you had all that data and crunched the numbers it might actually say that the sample was biased. But I think the author was way too quick to jump to conclusions.
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Shane Yeager
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The major problem with the math is the normal GIGO issue. Since the '60s onward, workers per household has been between 1.2 to 1.25.

The difference you project should be reduced by a factor of 4 or 5, leaving ~15% with a union member (rather than your projected 23% or the study's 20%) and ~20% to contain a gov't worker (rather than your projected 31% or the study's 25%.)

BO'R is an unmitigated blowhard who usually can't find his own ass with both hands and a map, but he's not as wrong as you're making him out to be. The assertion that the skewing was intentional rather than some artifact we aren't accounting for or a statistical anomaly is unsupported, I certainly agree.
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Erik Henry
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syeager wrote:
The major problem with the math is the normal GIGO issue. Since the '60s onward, workers per household has been between 1.2 to 1.25.

The difference you project should be reduced by a factor of 4 or 5, leaving ~15% with a union member (rather than your projected 23% or the study's 20%) and ~20% to contain a gov't worker (rather than your projected 31% or the study's 25%.)

BO'R is an unmitigated blowhard who usually can't find his own ass with both hands and a map, but he's not as wrong as you're making him out to be. The assertion that the skewing was intentional rather than some artifact we aren't accounting for or a statistical anomaly is unsupported, I certainly agree.

Thanks. I had found adults per household numbers around 1.95, but didn't think the workers per household would be this low. You're right, that drops my differences down significantly.
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