Statistics, precision, and slide rules

A number of Unitarian Universalist bloggers have reported on the recently released Pew Forum U.S. Religious Landscape survey. However…. I’d like to suggest everyone be more cautious about trying to calculate exact number of Unitarian Universalists in the United States based on this survey.

The survey reported that 0.3% of United States residents are, to use the Pew study’s exact terminology, “Unitarian (Universalist)”. First question I asked was, How accurate is this number? Well, we don’t know how accurate this number is because unfortunately the margin of error for the Unitarian Universalist subgroup is not reported. Can we extrapolate the margin of error from another subgroup which has approximately the same percentage, e.g., Hindus with 0.4% of U.S. residents? No, we can’t because a different survey methodology was used for Hindus — the survey boosted the sample size of certain low-incidence groups (Hindus, Buddhists, and Orthodox Christians) by calling additional pre-screened households.

It is worth noting that the worst margin of error they report for a religious subgroup is plus or minus 10.5%; this for Muslims, with 0.6% of the population, or twice the sample size for Unitarian Universalists. I would expect that the smaller the sample size, the larger the margin of error, so I suspect the margin of error for Unitarian Universalists is greater than or equal to 10.5%. But really we don’t even know the margin of error.

Another problem is revealed when you look at the actual survey instrument (see “Topline” on the Pew Web-report). The interviewers did not have “Unitarian Universalist” on their list of religious affiliations, and they did not ask any qualifying questions (as they did for many of the other religious affiliations). Since Pew uses the term “Unitarian (Universalists),” we don’t really know if all the respondents in this subgroup intended to report themselves as what we know as “Unitarian Universalists”. What if one of them happened to be a Primitive Baptist Universalist who said “Universalist” and got lumped into this subgroup? For the “Unitarian (Universalist)” subgroup, we can guess that n=105, which means just one PBU throws the figure off by approx. 1%. And then there are members of Unity Church, Universal Life Church, etc. — just one of each keeps upping the margin of error.

In addition, various bloggers have used numbers for the U.S. population that don’t really have a lot of significant digits. Given that imprecision, and without knowing the sample size or the margin of error for the UU subgroup, I’d have to say we simply should not use more than one significant digit when trying to estimate absolute number of Unitarian Universalists from the 0.3% figure given in the Pew survey. Let me put it this way: after reading the survey, the most I’d be willing to say is — this Pew Survey indicates that there are probably between 500,000 and 800,00 people in the United States who report themselves as Unitarians, Universalists, Unitarian Universalists, or similar-sounding name.

Several bloggers and other folks have taken an additional step, and tried to relate that very imprecise number to the number of Unitarian Universalists reported as legal members of congregations. What happens if we try to take that next step?

First, we have to question the accuracy of congregational membership figures reported to the Unitarian Universalist Association, because there is no standard methodology for determining membership (i.e., do you purge your membership list every year, or do you just accumulate “lost” members without question?);– for example, in one congregation I know of, after one minister left, an interim came in and slashed the number of members by over a third, although there were still the same number of people on the mailing list and in church on Sunday each week; in another example, one congregation dropped half their members the year before they went searching for a new minister just so they could drop down into a lower pay scale on the UUA salary guidelines. Furthermore, in all the congregations I have been associated with, there have been two to five times the number of certified members who consider themselves affiliated with the congregation and who show up perhaps once a year or even once every five years; in their minds they are affiliated with the congregation, but they are not reported as “certified members.”

Second, by now it should be clear that there is not a one-to-one correspondence between (a) certified members of Unitarian Universalist congregations, as reported to the UUA, and (b) people who report themselves as Unitarians/Universalists/Unitarian Universalists in surveys. We can count apples in this bin, and fruit that is round and orange in that bin, but it is not clear that there is a one-to-one mapping of apples to round orange fruit.

Therefore, if we’re going to be precise, the most we can say is this:– About 500,000 to 800,000 United States residents report themselves as Unitarians/Universalists/Unitarian Universalists on national surveys, whereas the UUA reports that its members congregations report that they have approximately 160,000 members. And the most I’m willing to conclude from all this is that more people (perhaps 2-3 times as many) report themselves to be Unitarians/Universalists/Unitarian Universalists than are reported as members of local congregations. But I already knew that, with about that degree of precision.

If you’ve ever used a slide rule, this all will make more sense, because slide rules users are more aware of how many significant digits you can actually use in a given calculation. And don’t tell me that slide rules are passe — actually, they’re considered quite cool in certain geeky sets. Speaking of geeks, I know I have some readers who are true geeks, who will have read this far just to see what I have to say about slide rules, and who will be able to offer corrections to my logic and my math. Go to it, geeks!

7 thoughts on “Statistics, precision, and slide rules

  1. h sofia

    hehe. I just read the Pew report about an hour or so ago (before you’d posted this), and my first thought was, “Muslims are only .6% of the population? That’s CRAZY TALK!” The 10.5% margin of error makes sense, but it renders the percentage they offered as pretty useless.

  2. Dan

    h sofia @ 1 — You write: ” ‘Muslims are only .6% of the population? That’s CRAZY TALK!’ ” Any survey is only as good as the survey instrument. My feeling was the survey was well-designed for determining how many people are in traditional Protestant denominations, and pretty good for determining Catholics, but beyond that things get a little fuzzy.

    Hey, but you and I are in the minority — much of the UU blogosphere seems to be trusting this report without much questioning.

  3. Elizabeth J. Barrett

    Thanks so much for your post. I actually was concerned when I first read the figures, because I began to worry that we should do something about this. I imagined thousands of UUs not able to find congregatons that would welcome and support them. Good God, we have to fix this problem right now! Let’s help these people find a home congregation by Easter/Spring!

    But really, all I can do is re-commit to my UU values of being compassionate and welcoming, working for peace and justice, celebrating the sacred, being the change I want to see in the world…and throwing is some forgiveness when I don’t live up to my own ideals.

  4. Comrade Kevin

    So far as numbers are concerned, yours are gigantic compared to we Friends. :-)

    The last estimate I saw said we have anywhere from 100,000 to 140,000 depending how you define “member”. Sound familiar?

  5. Elena Tabachnick

    I was just glad to read a post about this by someone who actually understands statistics – and is asking the questions that should always be asked of any numerical data. “Survey instrument!” “Margin of error!” “If you measured apples with one metric and oranges with another, how can ANY valid comparison can be made?”

    How refreshing.

    I used the following quote on the methods chapter of my (statistically inclined) Master’s thesis. It remains, as ever, apt:

    “It is hard to say anything truly nonsensical because it always sounds like it makes sense.” Marcel Duchamp


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