# A math challenge! June 3, 2015 10:36 AM   Subscribe

Already my mind does not lean towards mathematics, but this one has me absolutely stumped on where to begin.

For a grant, I need to come up with a targeted enrollment number and the gender/race/ethnicity demographics of that number. The actual study we would be piggybacking on will not give me their demographics until we are under contract, so I have to use what is publicly accessible on line.

Question:
Need a breakdown for 1,000 participants who own dogs based on 2010 US Census demographics and a Pew study report that shows only rates of white/black/hispanic pet owners.

Problem:
Even beyond the math, the form requires a number of American Indian/Alaska Native (AIAN), Asian, Native Hawaiian or other Pacific Islander (NHPI), mixed race (none of these have pet owning numbers on them), in addition to White, Black or African American, and Hispanic. AND gender (also found in census).

I will babysit this thread awhile to give information I have missed!
posted by lil' ears to Science & Nature (12 answers total)

Can you explain what your goal is here? I can't quite parse what you mean by "a targeted enrollment number and the gender/race/ethnicity demographics of that number." Do you mean, you are trying to enroll 1000 pet owners in some sort of program and you need to say how many of those 1000 pet owners are of each particular listed race?
posted by showbiz_liz at 10:50 AM on June 3, 2015

I've had to do similar demographic target population breakdowns for grants. I would assume that racial groups that don't have specific ownership rates have rates qual to the overall population. (For smaller racial groups, it won't make a huge absolute number difference with only 1000 participants.) I'd also assume that male and female are equal. It's much easier to justify null hypothesis rates than interpolated rates, IMO. (I might go as far as to target racial groups proportional to their ratio of the population, without paying attention to the ownership rates.)
posted by supercres at 10:55 AM on June 3, 2015 [2 favorites]

Since I would rather solve math problems online than work... I'll take a swag at this :)...

First, I would go with the data you have.

Of the 1000 households, how many are White, Black, Hispanic? Your census data gives you that and it's 720 white households (72.4% * 1000), 126 black households, and clicking on the Hispanic Population link, I would say 125 Hispanic households...

Then, of each of those households for data you have, how many of them have pets? That's where the Pew report comes in...
White house holds with pets = 720 * 64% = 461
Black households with pets = 126 * 30% = 38
Hispanic households with pets = 125 * 39% = 49

Now, how many households are left unaccounted for and what are you going to do with them? There's not too many... 720+126+125 = 971 households counted which means you have 29 uncounted. That seems low to me but this is all guess-timation.

You could do several things here. One approach would be to see if there is other data on the internet for pet ownership by race. [Here's a link -- scroll down a ways.] Another approach would be to use something like 35% as the "average non-white pet ownership percentage". Really since the number you're multiplying is small, it is probably not going to swing things all that much.

If you take 35%, then 29 households * 35% = 10 pet owning-households.

Anyway, that is how I would go about solving this problem. That was fun :), thanks, and now I have to go back to work :).
posted by elmay at 10:55 AM on June 3, 2015

I may be misunderstanding, but I don't think you can get that information from the data you were given. The Pew study likely screened out members of the races that you are interested in, so data for those populations isn't included in the report.

The easiest option is to divvy up enrollment based soley on the percentage of the population that fits into each category. Anything more involved than that would require more data. Is there data on pet ownership for the population as a whole (ie. ignoring race)? From that you could get a vague estimate of the total number of pet owners that are not white, Hispanic or black and create quotas based on their population proportions.

On preview, I have the same questions as showbiz_liz: do you want enrollment to reflect the demographics of the population as a whole or of pet owners? The first seems straightforward; the second seems impossible given the data.
posted by cost-cutting measures at 10:56 AM on June 3, 2015

Of the 1000 households, how many are White, Black, Hispanic? Your census data gives you that and it's 720 white households (72.4% * 1000), 126 black households, and clicking on the Hispanic Population link, I would say 125 Hispanic households...

This is the problem: "Hispanic" overlaps with both "White" and "Black."
posted by showbiz_liz at 10:57 AM on June 3, 2015 [3 favorites]

I think your strategy will be different depending on if this is a grant for pet stuff with an included question about racial breakdowns, or if it's a grant meant specifically to benefit people of certain races who own pets.

Assuming it's the former, I think you would be OK to say that 64% of whites and 38.45% of non-whites own pets. Given the data available, I don't think you can get more specific than that without some serious fudging or guessing.

I arrived at 38.45% with this math:

(726*.64)+274x=1000*.57

Because: of 1000 people, a representative sample would include 726 whites, 64% of whom own pets. That leave 274 non-white people, and x represents the unknown % of pet ownership in that group. But we know that of the entire 1000-person group, 57% own pets, so we can use some algebra to solve for x and figure out the % of nonwhite pet owners, which works out to about 38.45%.
posted by showbiz_liz at 11:09 AM on June 3, 2015

Response by poster: So many responses! Thanks all, let me weed through the math for each!

To give some info, the study will look at shared environments between dogs and owners, so I am trying to narrow down demographics of pet owners to the best of my ability.

New info I found is this:

"White respondents were most likely to own pets in 2011 (65.6 percent), followed by respondents in the Spanish/Hispanic category (62.5 percent), Asian/Pacific Islander/American Indian/Aleut Eskimo category (47.7 percent) and Black/African-American category (32.7 percent). "

Which is ridiculous in that they combine Asian/Pacific Islander/American Indian/Aleut Eskimo.

Thanks all!
posted by lil' ears at 11:25 AM on June 3, 2015

Ha, I was just going to post that, lil' ears.

Here's my comment, in case it's at all worthwhile:

Do you know a congenial veterinarian? They are likely to have a copy of the latest (2012, I think) "U.S. Pet Ownership & Demographics Sourcebook," which is expensive to buy, but probably has more demographics info than you can find elsewhere. ... And then I quoted the same info you found. It's possible the actual report narrows it down further. Basically, veterinarians want to be able to figure out demographics for their area as much as possible.
posted by taz at 11:43 AM on June 3, 2015 [2 favorites]

Response by poster: Yes, that sourcebook is SO expensive, but luckily we found that summary!

I appreciate you all helping me through this. I wanted to show you the work but it displays badly here, but here are the numbers (and divided the numbers by 2 for gender, rounding up for female and down for male). I had to make the (false) assumption that the hispanics were "white hispanics" since there was no other data:

white 763.7571529
black 62.343666
hispanics 105.0890679
asian 37.36531438
AI/AN 7.466434975
NHPI 1.375043877
MTO race 22.60332
posted by lil' ears at 12:52 PM on June 3, 2015 [1 favorite]

A company that sells marketing lists might be able to give you the overall demographics of people they have flagged as pet owners.
posted by Jacqueline at 1:05 PM on June 3, 2015

The race/ ethnicity question has two parts.

Is this person of Hispanic, Latino, or Spanish origin?
What is this person's race?

It's rather common for surveys to collapse/ combine racial categories when reporting results. This often happens when there are not enough respondents from certain racial and ethnic groups.

It wouldn't be strange to see white and non-whites as your demographic groups. In fact, someone well-versed in statistics/ survey methodology might be concerned if your grant contains the demographic information broken out too far. First, reporting on a "too small" sample is bad research. One wouldn't want to make decisions based off of too few samples or accidentally identify a respondent. Second, does the further breakdown of race/ethnicity provide additional and more accurate information? Finally, people tend to have OPINIONS about the "correct/ proper" way to infer data. You wouldn't want your reader to get hung up on the specifics of your back of the envelope calculation.

In short, I suggest making two different cross tabulation (or cross tabs) tables. White vs non white, and male vs female.
posted by oceano at 2:48 PM on June 3, 2015 [2 favorites]

oceano is correct, and the link is excellent. I do survey research, and while we keep track of small demographic groups, we do not report separate results for them.

For a small survey prospectus, do not worry too much about predicting the precise numbers, or carrying decimal places out too far -- your sampling procedures are unlikely to exactly nail the national census proportions, and this is not a problem. Besides, if you are riding along on a survey sampling and field operation run by experienced people, you will inherit their technically valid sample. Depending of mode of administration (phone/mail/web/mixed) and returns rates, this will vary from census (and that's okay).

The quality and coverage of the study-specific questions you craft, and the logic of the planned analysis is what matters.
posted by lathrop at 3:24 PM on June 3, 2015

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