Everyday Sociology Blog

Finding Success in Social Science Statistics Classes

By Janis Prince Inniss

Many students dread the thought of taking a statistics course and probably imagine that faculty foist it upon them as payback for having had to endure the class as students themselves. In reality, statistics courses are required for sociology and other social science students because they may be conducting their own research one day. If you go into a social science career one day, you will need to know statistical processes so that you can decide on what is most appropriate for your project.

Even if your social science career does not include conducting research, you will probably be exposed to lots of published research studies and the knowledge to interpret them remains important. Further, in our everyday lives we are exposed to lots of statistics in news articles and magazines. We often see and hear headlines such as:

· Candidate Y is likely to gain 45% of the vote.

· 25% of Americans think that XYZ is the right thing to do.

· 15.6% of men think ABC about their wives and girlfriends.

Wouldn’t it be handy to be able to get behind the numbers and use your statistical knowledge to assess this kind of information?

Yes, statistics courses are challenging for many of us and they demand substantial time and work. These courses tend to be unlike other classes—particularly in the social sciences—so I thought you might find the benefit of my experience, that of other colleagues, and some other students helpful.

You might want to do a basic math review (there are others, but one can be found at www.psych.nyu.edu/cohen/bmathrev.pdf) to see whether you have the skills needed for this class or just to refresh your skills. Although you’re not likely to have the high level math problems you dread, you will be at a real disadvantage if you don’t understand basic math.

Perhaps the most important suggestion is that you “keep-up” with your statistics class from the very beginning since “catching-up” later on is very difficult. (I recommend that you keep a notepad, journal, binder or some other source of blank paper handy when preparing for this class, along with a pencil and eraser. You should also have a calculator available; for many of these courses a fairly basic one will do.)

As you read each assigned chapter in your textbook, highlight or note concepts that seem important, and follow along with every mathematical calculation. This means doing the actual calculations, step-by-step, so that you get the same answers as they are laid out on the page of your textbook. Make a note of any places where you are unable to figure out how a calculation was performed. Ideally, you will read the assigned chapters before attending classes.

Although you might find some chapters difficult to follow, it is still important to try and go through the entire assignment before you attend the class in which the material will be discussed.

After class, go back to your textbook as a means of making sure that you’ve really got it. In this second go around of the readings and calculations, you might figure out how to do some that previously stumped you. If you haven’t, get help from your professor or teaching assistant. Quickly! Again, keeping up with this is important, because until the semester ends there will be new material and it all builds on what has come before.

Keep a few pages at the beginning, middle, or end of your notepaper for formulas and tricks you’ve discovered. Add formulas to this section of your notepaper as you encounter them. By the end of class, you will have a list of all the formulas you’ve learned. This is a handy reference tool. Some textbooks have done this work for you, but if you create your own list as you learn new things, with a glance, you can see what material you have already covered.

Every statistics textbook that I’m familiar with has problems at the end of each chapter. Sometimes, the back of the textbook has the correct answers to half of the problems—all the even ones or all the odd ones, usually. Sometimes, the textbook has answers to all of the problems. Do them! The more you do those exercises, the better, and more comfortable, you will become at solving such problems. More than likely your tests will have some version of these problems, so you’ll be receiving good practice for them.

Many students find it helpful to collaborate with classmates; form study groups and hold each other accountable for reading the material and doing the problems. You could do half of the problems and have a study partner do the other half so that you can discuss all of them when you meet. Explain concepts to each other; you’ll probably find that explaining material deepens your understanding of it. Caveat: all students will not be as conscientious as you are so be careful that you work with equally serious minded students.

If you follow my recommendations, you’ll have a softer landing in your social science statistics class and hopefully learn skills you’ll use for a lifetime. And if and when you go to your professor, having done so much preparation, you will create a wonderful impression.

Hourglass and Stick Figures

By Sally Raskoff

A recent article in the BBC News Magazine asked, “Does Christina Hendricks have a body women should aspire to?” The Daily Mail, a British newspaper, said “All women should aspire for hourglass size 14 figures, claims new equalities minister.”

If you haven’t seen the television show Mad Men you may not know that Ms. Hendricks plays a secretary whose silhouette is not typical for women in the media in 2010. The show is set in the cultural milieu of the 1950s-1960s, thus her hourglass curvy figure is certainly appropriate for the time depicted.

According to these articles, the British Equalities Minister, Lynne Featherstone, issued a statement that Ms. Hendricks’ body is “absolutely fabulous” and that more women of this shape should be role models – and fashion models. She explains her advocacy for more curvy women role models by pointing to the social pressures women and girls may feel when all they see in the media are very thin women.

Ms. Hendricks dimensions are reported to be 36-32-36 or 38-32-38, either way her waist is much smaller than her bust and hips. This hourglass shape is the standard in our culture, historically, even as recent media images of the ideal female figure show an more modern hourglass with a larger bust, tiny waist and straighter hips.

Many sociological studies have pointed to the interaction between the media depictions of women and the lives of real women and girls. Even public information, such as Wikipedia, acknowledges the body image issues of women in the United States and other western countries.

The importance of women’s waist-to-hip ratio has been studied across cultures in many Evolutionary Psychology studies. They tend to agree that a ratio between 0.7 and 1.2 is seen as most attractive across most cultures. (To get the waist-to-hip ratio, simply divide the waist measurement by the hip measurement.)

The results of girls and women trying to achieve this ideal is reflected in a variety of data. For example women, especially white women, are more likely than men to be significantly underweight. The classic film by Jean Kilbourne, Still Killing Us Softly, nicely depicts how advertising shapes and reinforces our image of the ideal female body in more ways than we realize.

The funny thing about all the buzz surrounding the British government’s validation of Ms. Hendricks’ size as ideal is that it focuses on yet another body type that is not necessarily accessible to most women. The BBC article notes that other women could attain her very small waist with as lot of exercise or by virtue of “lucky” natural endowments. The article depicts a corset with the caption “one way to an hour-glass figure,” perhaps jokingly implying that you could also squeeze yourself into that shape with this undergarment or by undergoing some form of surgery.

Women (and men) come in a variety of shapes and sizes. Focusing on one type as ideal over another may not be a step forward in valuing women as people instead of objects to be used and judged.

Why doesn’t the media employ a wider variety of women and men so that a more diverse picture of humanity is depicted?

Sociologically speaking, a Marxian theorist would point out the ownership of the media and its relationship to the economy. Perhaps media creators depict a narrow definition so that more products can be sold to the viewers and consumers who strive to attain such shapes.

A functionalist theorist might point out the adherence of the media to our norms of beauty, shaped as they have been by history and society as it adapts to an ever-changing environment.

An symbolic interactionist would focus on how the meaning inherent in media depictions has deep salience for the consumers of that media. Because people consume these images subconsciously and consciously, the images do have an effect on what it means to be a woman (or a man) in this society. Some people might feel like in order to be more feminine they need to live up to the images presented as normative for women, thus explaining the higher prevalence of eating disorders among girls and young women than for boys and men.

What more specific theories could speak to this issue? What can it identify that will help us better understand the issue – and identify potential solutions to these problems?

Uncommon Uses of Public Space

By Todd Schoepflin

In my last blog, I discussed Laud Humphreys’ research about men having sex in park bathrooms. I think one reason his research is so interesting is because having sex in public bathrooms is an unusual use of public space. Let’s face it: seeing someone comb their hair or apply makeup in a public bathroom isn’t very compelling. For that matter, a lot of things that occur in public view aren’t interesting. Not surprisingly, abnormal uses of public space often catch people’s attention.

For example, this summer the local media where I live devoted a lot of attention to a story about a couple who had sex on a picnic table in a park in the afternoon. I’m sure none of us are naïve enough to think people don’t have sex in a park. But we don’t actually hear about it on a regular basis. I suppose if we did, it wouldn’t be news. In this case, there were definitely some intriguing angles in the story.

First of all, children reportedly saw the couple having sex. Second, the woman, who was married, was actually charged with adultery. The article points out that it was the first adultery charge in New York State since 2006 and only the twelfth in the state since 1972. It was the lead story in a six o’clock news broadcast. The newscaster reported that the woman said her husband is transgender and that they hadn’t had sex in a long time. Along with these dramatic elements, I think the story is so captivating because the couple violated basic norms about the use of public space. It’s uncommon for people to have sex in a park in the daylight hours.

Lately, I’ve become interested in a very different use of public space: graffiti. It’s graffiti on a particular set of playground equipment that has really captured my interest. The playground you see pictured looks like any other playground, a perfect place to play for children. I spend a lot of time at this playground with my two-year-old son. When you get close to the equipment you notice it’s covered with graffiti. Some of it is innocent, like “Jimmy + Renee,” kind of what you expect to see at a playground. Some of it is much more edgy than I would expect, like “Worship Satan; Sniff Glue.”

Every time we go there is something new written. Recently I saw that someone wrote “Fall in love, not in line,” an interesting philosophical statement promoting love and cautioning against conformity. The rest of the graffiti is too obscene to describe in detail. Let’s just say that whoever defaced the playground is familiar with male and female anatomy.

I’m not easily offended, but it’s disgusting to me to see raunchy graffiti all over playground equipment that is designed for children. As soon as someone removes the graffiti, there’s new work to replace it. Although I can’t be sure who’s responsible, I picture young teenagers doing this at the playground. There are several questions I’d like to ask if I happened to catch them in the act: Why do you do this? For fun? To amuse your friends? Boredom? As a means to express yourself? Have you thought of using Twitter instead?

Okay, I wouldn’t ask the last question, but if you think about it, Twitter and graffiti do have one thing in common: they are both means of expression. One reason I blog is so that I can express my thoughts and ideas. Twitter, Facebook, and blogs like this one are uses of virtual public space.

While taking a walk in my neighborhood, I was thinking about the places we usually see graffiti: boarded up buildings, subway trains, and overpasses. Looking out onto the street, I wondered what’s stopping someone from directly tagging the street. I’ve never seen graffiti on roads. Have you? Assuming that people want an audience for their graffiti, a road would be as good a place as any. I found one story about someone who is using paint to vandalize public space in Minneapolis. Known as the “paint bomber,” the person splashes paint on bus shelters and highways. According to the article, the Minneapolis police department has an employee dedicated full time to investigating graffiti.

By the way, if you want to read an in-depth analysis of graffiti, check out Graffiti Lives, a book written by sociologist Gregory J. Snyder. Focusing on graffiti artists in New York City, Snyder points out many reasons why people engage in graffiti, including a need for vandalistic thrills, an urge to communicate one’s worth, and the desire to become famous. One of the many things I learned while reading this book is that Nike, Puma, and Adidas have hired prominent graffiti artists to design limited-edition sneakers. In a sense, these corporations have profited from people who are characterized by police and politicians as menaces to society.

The artist Spencer Tunick offers another example of using public space in an uncommon way. He’s been able to get hundreds (sometimes thousands) of volunteers to congregate for photographs, even though you have to be naked for the event! As you can see on the website, he has organized events in Dublin, Mexico City, Barcelona, Montreal, New York, and dozens of other places. As explained on the website, the point of assembling nude masses of people is not to emphasize sexuality, but rather to challenge conventional views of nudity and privacy.

I’ll finish with one more example of using public space. Speaker’s Corner is a place in a London park where anyone can go to talk about anything. You can just show up and start talking. I learned about it while looking for things to do in anticipation of a trip to London a few years ago. During my trip I ended up going there, thinking I might actually start speaking about something, but as it turned out I just listened to a strange fellow ramble on incoherently for about twenty minutes. Nonetheless, the idea of a public forum taking place in a park is pretty cool. In theory, we could all take turns airing our opinions in the parks in our communities, but most of us never will, perhaps because it’s not something that other people do on a regular basis.

Sex in parks during daylight, obscene graffiti on playgrounds, photographing nude groups of people, and expressing one’s views to strangers at a park are only four examples of atypical uses of public space. Can you think of some other examples?

Baby Showers as Rituals

By Janis Prince Inniss

Baby showers are such a common ritual in the U.S. that showers are even being held for American reporters covering the war in Iraq. I’ve been to quite a few baby showers; I’ve helped to plan some and hosted others. Many of the games I can live without: guessing when the baby will be born and guessing the baby’s weight are tolerable but some of the games played at these parties are not my cup of tea.

But like all showers or other gifting parties, my favorite part is the opening of the presents. No other kind of party has such cute stuff! The cutest little outfits. Teeny baby hats. Bath time toys. Little stuffed animals. Bumpers and sheets. Blankies. Many of the gifts correspond to a theme/motif if the parents have specified, and if the parents know the sex of the baby the gifts will be predominantly pink or blue. Even the party favors are cute--tiny pacifiers and bottles, and cakes shaped like diapers! The “entertainment” sometimes includes mothers sharing terrifying birthing stories.

Baby showers are another ritual that many of us attend, but we rarely think about their social significance (I discussed birthday party rituals here). Certainly, baby showers serve to welcome a baby, whether born or not. And in some cases they can help the parents and their friends and family get used to the idea of a pregnancy or even come to terms with an initially unwelcome pregnancy. Due to the ritualistic nature of such an event, there are specific elements we expect. What purposes do they serve?

At the most pragmatic level, baby showers provide many of the myriad items that babies need or that parents simply desire. When I was a little girl, it appeared to me that the only things you needed for babies were nappies (cloth diapers), loose-fitting tops, and a couple of (glass!) feeding bottles.

In the warmth and relative poverty of some of my neighborhoods growing up in Guyana, much more was superfluous. Why would someone who doesn’t walk wear shoes? In the heat, why bother with socks? Why dress up to stay at home? (Certainly, babies had Sunday best outfits too and were christened in their finest.) There was no need for car seats,or even for fancy carriers when a simple carrier could be fashioned from a piece of cloth. Most people didn’t have an entire bedroom to devote to a baby, so there was no need to decorate a nursery.

But in the U.S. today, babies seem to me synonymous with lots of paraphernalia: car seats for every stage of life, or car seats that morph from seat to carrier to stroller to luxury vehicles! And there are high chairs, folding strollers, deluxe strollers, jogging strollers, bouncy seats, designer clothing, mounds of toys, chests to store the toys, and a plethora of breastfeeding aids (breast pumps, breast feeding cushions, breast feeding bras, breast feeding wraps). In the context of all there is to buy for a little one, a shower seems like a great idea.

Of course, a shower is more than a ploy to get gifts. Isn’t it? But the baby shower ritual is not as universal as we might think.

I never thought much about baby showers and their meaning or whether they’re universal. I suppose the pragmatic aspect made sense to me and I left it at that. But a recent conversation with a relative caused me to think more about baby showers; my aunt said that she wasn’t used to baby showers occurring before babies are born and that she didn’t like the idea.

She explained that in England, these events—which are not actually called showers there—are given after a baby is born. (This is changing as American-style showers become more popular.) Why would you wait until then? I’m used to the model of North Americans doing everything to prepare for a baby’s arrival, often, many months before the birth. Often the only thing left to do is literally wait for the baby’s arrival. Clothes have been bought, washed and hung in the closet. Nurseries have been painted and decorated with murals and furniture. Appliances and other paraphernalia have been assembled.

But as my aunt pointed out, what happens with all of these plans in the event of the baby’s death? Perinatal (stillbirths and deaths in the first week of life) and neonatal (deaths in the first four weeks after birth) death do occur. In 2006, about 19,000 babies in the U.S. died in their first month alive. (Have a look at this post for some information on infant mortality in the U.S.)

Considering how much more dangerous childbirth was—both for mother and baby—it is not surprising that in some cultures and countries it would remain prudent to be cautious about preparing for a baby. Many Jewish Americans, for example, have baby showers only after they baby is born. Remnants of old childbirth fears—and the reality that there is an element of risk involved in pregnancy and birth—may explain why in some cultures it is still considered bad luck or improper to hold a shower or offer a baby gift for an unborn child. How do you think the social significance of a post-birth baby shower might differ from a shower held for a baby that hasn’t arrived yet?

Reality Television and Researching Children: Ethical Issues

By Karen Sternheimer

Are you a Kate Plus 8 fan? How about The Real Housewives of New Jersey? 19 Kids and Counting? These three reality shows, and many others, feature children either as central or occasional “characters.”

Sociologist Hilary Levey recently questioned some of the legal issues surrounding children on reality television in a USA Today op-ed. She points out that child actors have specific legal protections in states where child performers have traditionally worked, like California and New York, which mandate that a minimum of fifteen percent of a child’s income be placed in a trust account they can later access as adults. However, children on reality shows currently have no legal right to any money their show earns, nor have they typically been protected by child labor laws since they are technically not actors, as a Los Angeles Times story recently discussed.

In contrast to reality TV producers, researchers who study children and families in their homes adhere to specific ethical guidelines that may illuminate the debate about the ethics of children on reality television. (For a couple examples check out sociologist Arlie Russell Hochschild’s classic study, The Second Shift, and sociologist Annette Lareau’s Unequal Childhoods: Class, Race, and Family Life).

Researching children might involve surveys, experiments, or extended observations, which bear some similarities with reality television shows that involve children. In contrast to reality show producers, researchers mask the identity of the children they study and virtually never release their images publicly, let alone hours of video.

As Janis Prince Inniss wrote last year, universities and research institutes have Institutional Review Boards (IRBs) that monitor all studies its researchers conduct.

Anyone who has filed an application with their IRB knows that the process can be lengthy and sometimes stressful, as board members can require repeated clarifications about your research plan and its purpose. And yet this is demanding in order to protect both the subjects involved and, of course, protect the institution from any legal liability.

In most cases researchers are supposed to fully disclose the nature of the study and its purpose to all potential participants. If researchers plan to use any deception or mask the true purpose of the research—which they sometimes do—the researchers must prove to the IRB that this is absolutely necessary, and document a full list of worst-case-scenario contingency plans to help their subjects. At a minimum, researchers should debrief participants after the study is over, which includes telling them what the study was really about and make sure that all participants are physically and psychologically okay.

When applying for IRB approval, researchers must report whether their study includes populations considered uniquely vulnerable, such as minors. (Pregnant women, prisoners, and the disabled are considered vulnerable populations, too; pregnant women because of their physical condition and prisoners and the disabled because they might be easily coerced into participating in research).

To protect all participants, researchers are required to obtain informed consent, meaning that before agreeing to participate, an individual should be informed of all of the potential risks and benefits that their involvement in the study might bring. It is also meant to prevent people from being pressured into participating.

Special populations—like children—may fear repercussions from adults if they refuse to participate. Federal guidelines require not only parental consent, but also children’s assent—which means the child must agree to participate in the study too. Here are some of the guidelines, from the Department of Health and Human Services (HHS):

HHS will conduct or fund research in which the IRB finds that more than minimal risk to children is presented by an intervention or procedure that does not hold out the prospect of direct benefit for the individual subject, or by a monitoring procedure which is not likely to contribute to the well-being of the subject, only if the IRB finds that:

(a) The risk represents a minor increase over minimal risk;

(b) The intervention or procedure presents experiences to subjects that are reasonably commensurate with those inherent in their actual or expected medical, dental, psychological, social, or educational situations;

(c) The intervention or procedure is likely to yield generalizable knowledge about the subjects' disorder or condition which is of vital importance for the understanding or amelioration of the subjects' disorder or condition; and

(d) Adequate provisions are made for soliciting assent of the children and permission of their parents or guardians, as set forth in §46.408.

§46.407 Research not otherwise approvable which presents an opportunity to understand, prevent, or alleviate a serious problem affecting the health or welfare of children.

Basically, these guidelines require that any risks to children involved with research be as minimal as possible, and that children’s activities in the research process are generally similar to those in their normal lives.

Many reality shows focus on children’s everyday activities, as item (b) above discusses. But critics have asked what risks might come with their participation. Having cameras record a child’s temper tantrum or struggles with potty training might seem innocuous, but it raises questions about a child’s right to privacy. Adults would almost certainly never allow a camera to follow them into a bathroom, and might feel more empowered to ask the crew to turn off the cameras during an emotionally difficult time.

Item (c) raises series distinctions between research and reality television. While risks of research could be outweighed by the benefits of the knowledge researchers gain about human behavior, reality television makes no claim to provide social benefits aside from entertainment. Yes, we might learn what it is like for a family to have an unusually large number of children, but most programs don’t necessarily add to our body of knowledge.

Are the potential risks children might face through participating in reality television worth the financial gain? The answer is not clear cut. Yes, their parents might be able to afford to provide more for them materially. The children could get to travel and partake in many kid-friendly adventures they wouldn’t get to do otherwise.

And yet concerns about physical injury during the 2007 filming of Kid Nation and the potential psychological effects of living in front of cameras remain important questions. What other ethical concerns arise from children appearing on reality television?

A Closer Look at Interracial Marriage Statistics

By Janis Prince Inniss

“Interracial Marriages at an all time high, study says” – CNN

“Study: 1 in 7 New U.S. Marriages is Interracial” – CBS News

“Interracial marriage: more than double the ‘rate in the 1980s’” – The Christian Science Monitor

“Interracial Marriage More Common Than Ever, but Black Women Still Lag, Pew Survey Shows One in Six New Marriages Now Between People of Different Colors” - ABC News

“After 40 years, interracial marriage flourishing, Since landmark 1967 ruling, unions have moved from radical to everyday” - MSNBC

“New Study Finds There Are More Interracial Marriages Than Ever” – Glamour magazine

Armed with these headlines alone, what can we surmise about interracial marriage in the U.S.? Given that such unions are “flourishing,” “common,” and at “an all time high,” I might assume that the people I know are unusual because they are not in interracial relationships.

But let’s go beyond the headlines. In fact, let’s go to the source of many of these headlines --a recent Pew Research Center analysis of U.S. Census Bureau data. The data show that 14.6 percent of all new marriages in the U.S. occurred between people of differing ethnicities/races. The distinction between new marriages and already married people is an important one to pay attention to because it tells us what population the statistic refers to; without keeping that in mind, the numbers tell us nothing.

So back to the statistic--14.6 percent – because it refers to new marriages, and new marriages are only a portion of all marriages..

It is hard to qualify 14.6 percent or 8.0 percent of almost anything as being abundant; the bottom line regarding interracial marriage in the U.S. is that it remains highly unusual. Yet the media has been very busy reporting results of the Pew Research Center on interracial marriage.

What some of these headlines highlight is a trend. They point out that although intermarriages are a small portion of all marriages, over the past 30 years, the portion of new and ongoing marriages has increased drastically. Notice that some headlines highlight this comparison: In 1980, 3.2 percent of all married people were in interracial relationships, but 8.0 percent were in 2010. And the 14.6 percent of new marriages that are interracial is up from 6.7of new marriages in percent in 2008.

In both cases, it is legitimate to refer to current rates of interracial marriage as being “at an all time high” and indeed they are now “more than double” what they were. But hopefully, with some training, either of these kinds of qualifiers will prompt you to ask, “High? How high?” and “More than double what number?” Unless we think about and get this kind of detail, we are left with the impression that interracial marriage has swept the land!

As we consider these statistics, it’s also important to remember that interracial marriages were illegal in some states in the U.S. until 1967, with the U.S. Supreme Court decision in the Loving v. Virginia case. Given the social and legal context of the day, even without knowledge of the data of the last 30 years, would you have guessed that there was a rash of interracial marriages in 1968, 1969, or 1970? Or even in 1977, ten years after the Supreme Court decision? No. Therefore, baseline data on interracial marriage reflects the scarcity of this phenomenon.

And because of that, even relatively small increases can be described as indicative of big change. For example, 2 percent is double 1 percent, but 2 percent of something still isn’t a lot. Increases from 3.2 percent to 8.0 percent, and from 6.7 percent to 14.6 percent represent the same kind of change.

At the end of the last post on interracial marriage, I wrote, “Regarding young Mr. Smith, like 84.5 percent of people in his racial/ethnic group, he is marrying within his race.” The first chart in that piece contained the answer to Mr. Smith’s racial identity; unlike 15.5 percent of Blacks, he is not entering an interracial marriage. That same chart also highlights the point—displaying data for four racial/ethnic groups—that most newlyweds are not marrying people of a different racial/ethnic background.

Take a look at the chart below:

Initially, as I looked at the bars representing black men next to the bar representing black women, I was perplexed. Why? Because the proportions are so similar; it looked to me like black men and black women marry “out” at the same rate, and to the same other race/ethnicity. But how is that possible when we know from an even earlier post focusing on black/white interracial relationships (see chart below) that there are far more white women and black men married than there are white men and black women?

I expected to see that jump out at me in the bar chart above and was surprised to see such similarities. Do you see the fault in my initial thinking? It’s the issue of the population again. Data in the bar chart are of blacks who “out-married”, while the line graph compares raw numbers of black/white couples. Therefore, to make a direct comparison I had to remind myself that the shaded portion of the bar chart that represents black marriages to whites represents about 100,000 women but more than 300,000 black men.

Source: U.S. Census Bureau, Table 59 and MS-3.

Blue line represents black husband/white wife.

Red line represents white husband/black wife.

Both the headlines and the data about interracial marriage remind us that we need to think critically about what numbers we hear about really tell us about social change.