Press outlets have been covering a report by the Williams Institute (based at UCLA), a research organization collecting data on demographic information on sexual orientation and gender identity. The quotes in this post come from **this summary from PBS****.**

The new study has estimated the number of LGBTQ adults in the U.S. who identify as nonbinary. (Nonbinary is a term that is often used to describe people whose gender identities are more than the man/woman category; some nonbinary people use they/them pronouns.) It's important to estimate how many U.S. adults identify as nonbinary (as well as other sexual- and gender-minority identities) because anti-discrimination laws potentially affect them. PBS reports that:

Nonbinary people are part of a “growing subgroup” of the LGBTQ population, Wilson said, adding there’s been greater visibility for nonbinary people. More and more celebrities, like singers Demi Lovato and Sam Smith, and actors Indya Moore and Amandla Stenberg, have talked about identifying themselves as nonbinary or in related terms.

Here's a portion of the PBS summary:

According to the study, which focused on people ages 18 to 60, nonbinary people make up about 11 percent of the adult LGBTQ population in the country. The study builds on the work of two prior surveys — one on trans adults, [TransPop] the other on cisgender LGBTQ adults [Generations]— to provide more comprehensive data on nonbinary people, a historically underresearched subgroup.

When the researchers extrapolated out form this subsample, they concluded that

There are about 1.2 million LGBTQ adults in the U.S. who are nonbinary.

The data in this report constitute a frequency claim, because they are estimating the level of one variable (that is, nonbinary identity).

First let's talk about the precision of these estimates. The report from the Williams Institute (**here**) includes 95% CIs for the estimates. For example, the two estimates from the PBS story were presented this way:

Number of nonbinary LGBTQ adults in the U.S., including transgender and cisgender people N [95% CI] | 1,219,000 [1,000,000 - 1,481,000] |

% [95% CI] of LGBTQ adult population | 11.1 [9.3, 13.2] |

a) In your own words, describe what the first CI means. Use this definition and template to help you: *The 95% CI is meant to capture the true value in the population 95% of the time*. *The true value in the population might be as low as ____ or as high as ____. *

b) Sometimes the 95% CI misses the true value in the population. What percentage of the time will the CI miss?

Next lets' talk about external validity (generalizability) and sampling. As you consider these estimates keep in mind that there is a distinction between estimating the number of *all U.S. adults* who identify as non-binary and the number of *U.S. LGBTQ adults* who identify as non-binary. These values may be different.

c) Given what you've read so far, what seems to be the population of interest of this study?

To know if the sample is generalizable, you need to know how they obtained the sample. The PBS summary doesn't say anything about the sampling method used in this study, and neither does the **Williams Institute report**. To locate information about the sampling, I had to go to the methods sections of the two studies on which the nonbinary study is based: The **TransPop study** (which studied a sample of transgender U.S. adults) and the **Generations study** (which studied a sample of LGBTQ U.S. adults).

In these methods sections, they say that these two studies (TransPop and Generations) worked with the Gallup organization to recruit nationally representative samples of transgender and LGBTQ adults. Gallup performs a Daily Tracking Survey in which they call a national probability sample of 1000 adults, almost every day of the year. These adults are sampled using random-digit dialing, including both landline and cell phone numbers. Gallup asks a variety of questions about well-being, political attitudes, and economic situations. At the end of each telephone survey, the interviewer asks, “I have one final question we are asking only for statistical purposes. Do you, personally, identify as lesbian, gay, bisexual, or transgender?” Gallup retained the records for people who said *yes* to this question over one year, and the Generations and TransPop studies contacted these folks later. At this second contact, researchers checked to be sure each person was eligible for the Generations or TransPop study, and if they were, the researchers sent them a survey by mail or email. To be eligible, people had to identify as sexual minority or transgender, be within certain age ranges, and be able to complete surveys in English.

After people were recruited into the TransPop and Generations studies in this way, they were asked multiple survey questions, including the target question about whether they identified as nonbinary.

d) In your own words, explain why the procedure used above is likely to lead to a probability (in other words, a generalizable, or externally-valid) sample of LGBTQ adults in the United States.

e) Reading the description above, which type of random was used here--random sampling or random assignment?

f) To reiterate, the study concluded that about 11% of LGBTQ people in the United States identify as nonbinary. What method could we use to estimate the percentage of *all* people in the United States identify as nonbinary?

g) What do you predict might happen to the estimate of nonbinary people in the U.S. if they redid this study 20 years in the future?

**Suggested Answers**

a) The 95% CI is meant to capture the true value in the population 95% of the time. The true value in the population might be as low as 1 million or as high as 1.48 million. Importantly, our CI may have missed the true population mean. We don't know if it missed it or not, but we know the probability that our CI missed it--see question b)!

b) the 95% CI will miss the population mean in 5% of cases.

More information: If we replicated the study, the new estimate and 95% CI will be a little bit different from the first one. But we'd still expect that the replication estimate of the number of nonbinary adults will be between 1 million and 1.48 million. We'd be surprised if our new estimate was a lot lower or a lot higher than this range.

c) The population of interest is LGBTQ adults in the United States (who have access to a cell phone or landline)

d) The Gallup sample is generalizable because their Daily Tracking Survey goes out to a random sample U.S. adults. Any LGBTQ folks that are called in that survey are therefore also a random sample, and random samples are generalizable.

e) They used random sampling. (As a reminder, random assignment is used in experiments, to assign participants to different groups.)

f) One method could be to ask directly of a random sample of US adults. For example, Gallup could potentially add a nonbinary identity question to their Daily Tracking Survey for one year.

Another method was the one used in the present study. Gallup learned that 3.5% of their Daily Tracking Survey sample answered yes to the LGBTQ question, and then, of that subsample, a certain percentage (about 11%) identified as nonbinary. After adjusting weights, they got a percentage, (maybe around .05%) which they multiplied by the entire U.S. adult population, to produce the estimate that about 1,219,000 adults (or between 1 and 1.48 million) identify as nonbinary. To see some of the statistics I quoted here, visit this **page**)

g) Answers will vary