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Author Topic: Let's Talk Statistics
Shan
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Well, okay - I'll ask some questions, and you talk!

Per Capita - an average per person, right? How does this work? And why is it better for figuring out data on such things as rural versus urban poverty?

For example:

County A has 100 people - rural.

County B has 1000 people - urban.

County A has 8 people that live at 80% of the federal poverty level.

County B has 20 people that live at 80% of the federal poverty level.

Which county has the most need and why?

(And no - this is NOT homework.)

*grin*

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fugu13
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Yes, per capita means per person. Its better for figuring out poverty because if you just looked at total wealth, people in comparably sized urban areas will always have more, simply because there are more people there.

We don't have enough information to determine need. If this is an "all else being equal" problem, then clearly County B. All else is never equal, though, when it comes to such populations [Wink] .

However, you haven't performed a per capita evaluation. Say both counties have 40 people total, and that all the people not living at 80% of poverty level average out at 160% poverty level.

Then the per capita poverty level in County A is 1.44, and the per capita poverty level in County B is 1.2, and we clearly see which is worse off (by a lot, for such small counties [Wink] ).

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Shan
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So, on an "if all else being equal", then county B has more need because they have more people, regardless that the percentage of people at that poverty level would be less?

And how did you figure out the per capita? What formula did you use?

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fugu13
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Well, its not strictly speaking the best application to talk of something like that being a per capita, you usually speak of something you total.

I'm silly, btw, I completely neglected the total population values you posted. I thought they were the same when I read through, in which case it is the most number of people who has the most need.

However, once we introduce even the slightest complexity (such as the two population sizes), who has the most need is a subjective determination which can be talked about in many different ways. It could be an absolute number of people in need. It could be which county is overall poorer per capita, it could be the place with the fewest rich people (providing charity).

As for how I obtained my numbers based on 40 people total, I simply used basic averaging: (1.6*(40-number@80%) + .8 * (number@80%))/40 . Even if the actual values for other people are all over the place, their total will equal 1.6*their number, because that's the definition of an average.

Applying the same procedure to your populations (assuming the 1.6 average for other people), we arrive at a "need per capita" in County A to be 1.536, and in County B to be 1.584. This is a difference so miniscule as to be irrelevant in determining which county has the greatest need; most likely we'd just go with the county with the most people in need.

Per capita is only the grossest measure -- an average. It tells us where the center of a population is while telling us little about the distribution. However, it is generally quite useful in large populations for a simple reason -- most large populations tend to be normally distributed. This allows us to make certain assumptions about what a per capita average means, absent other information (though we also need at least a vague estimate of the deviation of such a population).

There's nothing magic about a per capita number; its often useful. For instance, per capita income will let us have a vague measure of what people in a population make -- there are other measures, like median and mode, of course, but the mean will give a better idea in some ways (though there are occasions each is useful).

Per capita is mostly used because its easy, and because its a starting point. No effective statistical analysis would use it as the only data for determining allocation of some kind (including data about the distribution; certain distributions are wholly characterized by the mean).

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alluvion
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Just to clarify:

What does "80% of the federal poverty level" mean?

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fugu13
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That the measure of someone's economic status (pretty much income) is at 80% of what the federal government thinks the measure of the borderline between poverty and non-poverty is.

To put some of what I've said above another way: for any trivial method of determining need, I can come up with a simple, reasonable seeming example for which that method of determining need doesn't seem particularly well-suited.

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Shan
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So, fugu - if you were distributing funds based on need determined by, say, three different countywide poverty indicators for each county in a state, how would you do it?

What are some ways to account for the difference between rural and urban poverty indicators.

It's pretty standard that any urban area will have both pockets of really wealthy and pockets of really poor - would that not average out?

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alluvion
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wait. so 80% of the "federal poverty level" means 20% under the poverty line?

This seems like a confusing definition. Does it matter by what degree a person falls short or surpasses the "poverty" threshold? and, how so?

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fugu13
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Well, they would average out in the average if they were approximately equally distributed about the mean of the other data, but their existence would affect the variance of the distribution.

As for distributing funds based on need on a per-county basis in a state, ideally I'd first do some in-depth case studies by county before choosing factors.

Absent that, though, it'd greatly depend on what data I had access to. I'd likely use a combination of number below a certain level (assuming I had access to that data), which is the most important part, median income in the population (somewhat a measure of how much the population is capable of "helping itself" in interstitial ways), and some measure of existing infrastructure (likely based on total local government revenues and certain sorts of outlays).

The most important would be the number of poor people, but it wouldn't be an absolute determining factor. For instance, 20 poor people out of 100 need more help than 25 poor people out of 10,000, almost certainly.

And the amount of aid wouldn't just be dependent on those factors, either, it would be done in large part by matching on in-county outlays, the amount of matching determined in large part by the latter two factors.

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fugu13
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You'd rather 80% of the poverty level meant, what, 30% under the poverty line? I'm confused as to how the definition is confusing.

And it matters because in many areas its perfectly possible to survive, if be poor, at 80% of the federal poverty level. The federal poverty level is a massive average across the entire nation.

And considering someone earning 20% of the federal poverty level would be starving and homeless (absent aid) while someone earning 80% wouldn't be, I'd say it matters a fair bit. Can you imagine telling someone earning that 20% "well, it wouldn't matter much to you if you were earning four times as much, because you'd still be poor"?

Oh, and the level I discuss in my previous post wouldn't be the federal poverty level, it would be done on a per-county basis using standard of living measures with local costs (most notably housing) taken into account.

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Jhai
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The Census Bureau (of the U.S.) breaks down their historical poverty data into two columns: people who are below 125% of the poverty level, and people who are between 125% and 100% of the poverty level, classified as the "near poor."

http://www.census.gov/hhes/poverty/histpov/hstpov6.html

"Below 125% of the poverty level" basically means that you're somewhat below the poverty level--you aren't borderline, in otherwords.

How to measure poverty has always been a question researchers argue about. How you define it really depends on what kind of information will be helpful to your study.
The Census Bureau has one way, but there are other ways to measure poverty:

http://tinyurl.com/9gtge
http://tinyurl.com/74fpy

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Shan
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You're a wealth of information, fugu!

Okay - let me go with this one here - I am appreciating thinking this through . . . it plays into some volunteer work I am doing, and I want to speak correctly, not just intuitively.

Assuming I have a population that is already receiving a certain set of services based on substantiated low-income, and with demonstrated need (i.e., underserved population base), then the next step would be to review the county in entirety for the value they could add to the currently existing program? Like infrastructure, in-place collaborations, etc?


And then, you say:

"The most important would be the number of poor people, but it wouldn't be an absolute determining factor. For instance, 20 poor people out of 100 need more help than 25 poor people out of 10,000, almost certainly."

There is someone in our group arguing the exact opposite - based on the urban vs. rural difference in poverty level. Essentially saying that assigning fewer funds to an area that scored low based on demonstrated need is incorrect, because the size of the population was not taken into account . . .

I am sure there is a middle ground and we will find it, but this is curious to me -

My head keeps saying that if county A has 8% population that needs assistance while county B has only 2% population in that same bracket, then county A gets the most funds.

Anyways - this is how my reasoning goes from the grantwriting days - and my reasoning worked well then, as I had a 90% return rate on all my grants. But I am really curious to see if there is a way to look more carefully at the urban vs the rural setting.

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alluvion
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fugu's a freaking moron, if you ask me.

*wanders off to make a real post and makes a 180 degree turn*

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Jhai
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Well, when you're talking about throwing money at a problem, you want to make sure that money is going to be truly helpful.

quote:

"The most important would be the number of poor people, but it wouldn't be an absolute determining factor. For instance, 20 poor people out of 100 need more help than 25 poor people out of 10,000, almost certainly."

Targeting those 20 people would almost certainly be easier than targeting the 25 people lost in a sea of 10,000. Plus you need to consider how the community as a whole is affected: if 20% of a community is below the poverty line, I would say that's a serious problem. If 25 people in a town of 10K are below the poverty line, I'd probably throw a party for the mayor (or whoever was responsible for such a low number of people in poverty, per capita [Smile] ).

But if you look at some more realistic numbers... I'll take your numbers of 2% and 8%. Say 2% of the 10K town is in poverty (200 people), versus 8% of the rural community of 100 people (8 people total). Looking at the straight percetages, then you'd say that the rural community needs more help. However, when you take into account the size of the populations, you realize that there are far more people in need in the town than in the rural community.

Now, I don't know much about how, exactly, social workers help out the poor, but I imagine that you could have one person working full time to help the poor people in the rural community find better jobs, or go back to school, or whatever they need help with.

Whereas one social worker could not cover the needs of the 200 poor people in the town--you'd need to send more resources (and money) there if you wanted to do a good job.

So I think that your coworker was correct in saying that, IN GENERAL, it's important to look at the size of the population. More data is (almost) always better in situations like these.

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alluvion
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shan,

*looks around for twerpy fugu and laces up combat boots*

I don't really understand what that 80% of "federal poverty" number was supposed to represent.

There's also a question of a missing goal. What is the distribution (however it is earmarked) of the funds supposed to achieve?

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Shan
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It means that folks are really stinking dirt poor, Mike - for the sake of using round numbers, if a family of four is considered officially poor with an income if $1000, then a similar family making $800 are even poorer.

Jhai - the 8% and 2% were based on the samples in the first post of:

"County A has 100 people - rural.

County B has 1000 people - urban.

County A has 8 people that live at 80% of the federal poverty level.

County B has 20 people that live at 80% of the federal poverty level.

Which county has the most need and why?"

Just an interesting conundrum for a little community network funder. Pretty hypothetical - but it is very interesting to hear the variety of opinions as to how/why funds should be used amongst a group of volunteers.

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fugu13
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quote:
That the measure of someone's economic status (pretty much income) is at 80% of what the federal government thinks the measure of the borderline between poverty and non-poverty is.
What part of this explanation didn't you understand, you haven't clarified your misunderstanding one iota, and without an understanding of your misunderstanding, resolution is unlikely to occur. I've already clarified why it matters greatly how far under the poverty limit someone is.

Here's a good illustration of why allocating funds based purely on a percent of total population below <insert poverty determinant here> isn't the best idea -- an extreme case, but not all that much.

Say we have a county (with a city within it) with, oh, two million people, and ten percent below our limit. So that's two hundred thousand people in need of assistance.

Then we have a county with ten thousand people in it, but twenty percent are below the poverty line, or two thousand people.

The latter county shouldn't receive more than a small fraction of the funds the former county receives -- despite having twice the percentage of poor people. It just doesn't make sense to allocate anywhere near as much for two thousand people as one is allocating for two hundred thousand people.

Also, I'd like to reiterate the importance of taking into account cost of living differences between counties. Housing is one of the single biggest and most variant parts of any poor person's expenses. It can cost $200 a month for decent living in rural areas that one couldn't get for $500 a month in a city (and more extreme cases, but that's not a particularly unusual distribution at all). That $300 a month can very well be the difference between a person who needs immediate aid and a person who's getting along decently. Being poor does not occur at the same level across a state, and acting like it does will only result in cities being underfunded (since many poor people will be treated as just over poor, the average not adequately dealing with the higher cost of living in the city) in proportion to the rural areas.

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alluvion
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and, what are the funds supposed to accomplish?
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fugu13
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That is an important question, but as I'm not the one asking the question I can't answer it; I have tried to keep my answers fairly generally applicable to the various ways in which funds could be used to alleviate/fight/reduce/ameliorate poverty.
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alluvion
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fugu,

do you have any suggestions? I think there are ways to allocate resources in a logical and strategical fashion so as to garner the best return, but the societal goal should be well-articulated, no?

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Shan
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Absolutely, fugu - cost of living, especially housing costs, are big considerations. I'm not disregarding them at all.

(And I personally don't know anyone that would ever make a decision like that based on a single determinant [Smile] - professionally or privately . . . I dumbed down my original example for sake of simplicity. Would that life could be that simple, neh?)

But it's definitely an interesting conundrum - depending on the particular task/goal and population, different variables will make more or less sense.

Anyways, I was very curious about the use of just population "numbers" versus "percent" - if I am understanding correctly, it would be erroneous if that were the only variable used? But not necessarily if other variables were used in conjunction . . .

*yawn*

Sorry, getting on to beddy-bye time. Thanks for all the good thoughts, folks - whoever thought statistics could be so interesting? [Big Grin]

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fugu13
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Neither pure numbers nor percentage is a perfect measure of a county's "need" for aid. A county with a higher number of people in poverty needs more aid if it wishes to make the same difference, particularly for certain sorts of aid (direct and indirect payments, for instance, which shouldn't really be determined on a per county basis anyways), but a county with a much higher percentage of people in poverty will have a harder time dealing with its poor people absent disproportionate aid even if the absolute number of poor people is not that great.

And yes, just depending on one (or even both) of those variables would be a bad thing. Some counties will already have fairly effective programs tackling whatever the funds were designed to accomplish, while others will have had additional problems preventing the tackling of poverty, and everything in between.

alluvion: there are lots of possibilities. To name a few: increase income for people below (whatever chosen) poverty line; ensure housing for pb(wc)pl; provide general education for pb(wc)pl; provide education for kids of pb(wc)pl; provide medical services for pb(wc)pl; et cetera.

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