Friends
When it comes to friendships, quality arguably beats quantity. Most of us would rather have meaningful connections with 3 or 4 people than a thousand followers on Twitter. Indeed, studies have repeatedly linked supportive friendships to better mental and physical health, greater longevity, etc.
Although evidence suggests that having as few as 1 or 2 close friends is beneficial, it's hard to shake the idea that the more friends one has, the better. Which raises a question: How many friends can one have? Strangely enough, there seems to be an answer. It's called Dunbar's number, and it's 150. The theory behind this number is that human brains are wired in such a way that the maximum number of stable social relationships we can keep track of is about 150. (Later I'll discuss whether "stable social relationships" means the same thing as "friendships.") Dunbar's number has been widely discussed by scholars as well as journalists (e.g., Malcom Gladwell, in The Tipping Point), and it has been applied to the design of office spaces, social media groups, strategies for professional networking, and online security systems for recognizing bots.
I'm writing about Dunbar's number because it has been the target of heated debate among scholars over the past three months – and because it illustrates two of the most common ways that statistics are misused in research.
Let’s start with the origins of this number. Why 150, as opposed to, say, 127 or 200? On the face of it, any specific number sounds implausible.
Roughly three decades ago, Robin Dunbar, a professor of evolutionary psychology at Oxford University, was examining a graph showing that the brain sizes of primates are correlated with the sizes of the social groups they form – i.e., the larger the brains, the larger the groups. Dunbar noticed that when human brains are added to the graph, one would predict that humans tend to form groups of 148 people, a number that Dunbar rounded up to 150. He then gathered evidence that across many times and places, stable social groups do tend to be about this size. The examples he cites include hunter-gatherer societies, Anglo-Saxon villages, church congregations, unit sizes in professional armies, and online gaming communities.
In brief, Dunbar started with data on various primate species, generated a prediction about humans, then found evidence in support of the prediction. The final step was to fold this evidence into a theory. In an influential 1992 article, Dunbar noted that it's cognitively demanding to maintain close social relationships. You have to keep track of what's going on with each person, their struggles and successes, their likes and dislikes, etc. The area of the brain responsible for this kind of social cognition is the neocortex, the outermost three-quarters of your brain (and the most recent area to evolve). The primate data that Dunbar relied on most heavily shows a correlation between the size of the neocortex in each species of primate and the size of their social groups. Crudely speaking, the more the neocortex you have, the more capable you are of maintaining friendships.
That 150 figure should seem a little more plausible now. And yet, you might be wondering: What is it exactly that's limited to about 150? I've looked, and nobody, including Dunbar, has ever been completely clear about that. Dunbar uses phrases like "stable social relationships", "quality relationships", "natural social groups", "meaningful friendships", and "people you would not feel embarrassed about joining uninvited for a drink if you happened to bump into them in a bar." He has noted, helpfully, that these people would be more than just Twitter followers or acquaintances. At the same time, it's confusing that in some places he refers repeatedly to "150 friends" while in others he distinguishes between "intimate friendships" (about 5), "friendships" (about 50), and that larger group of 150 which he tags with a variety of names but has never explicitly defined.
I feel like I have a rough sense of what Dunbar has in mind, even if a definition is lacking. So, for the moment, I'm willing to say (as Dunbar and others say) that Dunbar's number tells us the maximum number of friends we can have, and that this number excludes acquaintances, formal contractual relationships, social media followers, etc. I'll return to the definitional issue near the end.
In May of this year, a team of Swedish researchers published a rebuttal to Dunbar's work, touching off a debate that has yet to be resolved. Two of the key concerns raised by the Swiss team are statistical, and they illustrate classic problems in the use of stats. Happily, you don't need a background in statistics to understand these problems.
1. The confidence intervals for Dunbar's number are huge.
A confidence interval is a kind of estimate. Roughly, it estimates the range of values you would probably obtain if you repeated the same measurement with different samples from the same population.
Researchers define "probably" in mathematical terms. By convention, it's often defined as "95% of the time". Thus, a 95% confidence interval estimates the range of values you would obtain 95% of the time if you repeated the same measurement with different samples.
Here's a simple example: In 2008, the final pre-election Gallup Poll predicted that Barack Obama would win the U.S. presidency with 55% of the popular vote. The 95% confidence interval for this prediction was 53% to 57%. (In other words, the margin of error was +/- 2 percentage points.) President Obama eventually received 52.9% of the popular vote, which actually falls slightly outside the margin of error (i.e., by 0.1%). But, as you can see from this example, the confidence interval was quite small to begin with. The Gallup Poll gave us high confidence in a narrow range of possible outcomes. In theory, any outcome could've occurred, but given the confidence intervals that Gallup calculated, it's extremely unlikely that President Obama would've obtained, say, 30% or 80% of the popular vote.
Back to Dunbar's number. Remember that Dunbar looked at graphs of relationships between primate brain size and social groups, then predicted that human social groups don't exceed about 150. The Swedish team replicated Dunbar's work by means of more thorough methods. They used larger samples, as well as multiple approaches to measuring the size of primate brains (brain volume, brain weight, proportion of brain represented by the neocortex, etc.), and they applied different kinds of statistical models.
The results were bad news for Dunbar. Predictions of human social group size varied widely, and the confidence intervals were much too large to be meaningful. For example, in one analysis focusing on proportional size of neocortex, the predicted human group size was 108.6. That doesn't sound too terribly different from from Dunbar's number, but the 95% confidence interval was 4.6 to 520! In other words, if we kept on gathering data, most the time we would expect to find human social group sizes of somewhere between 4.6 and 520 people. That’s not a useful prediction.
Other analyses by the Swedish team showed much lower estimates of group size but comparably wide confidence intervals. (In a few cases, the estimates were larger. For example, in response to a criticism by Dunbar, the Swedish team reran their analyses as per Dunbar's recommendation and obtained an average group size of 289.8, with a 95% confidence interval of 226 to 371.6.)
In sum, huge confidence intervals in these data prevent us from learning much about human social groups.
As you may have guessed, there's a trade-off between "confidence", in the sense I'm using it here, and the specificity of the estimates. I can estimate, with more than 99% confidence, you have somewhere between 1 and 100 million friends. However, I would have very little confidence in the estimate that you have between 4 and 6 friends. High confidence intervals (e.g., 95%) are often used in science, because, to put it very crudely, we would rather make accurate but vague statements as opposed to precise statements that are wrong.
The fact that the Swedish team came up with different estimates each time they adjusted their methods, somewhat independent of the confidence intervals, leads us to the second problem they found with Dunbar's number:
2. Dunbar's number changes every time it's measured.
As the Swedish team pointed out, Dunbar's number is sometimes based on data for apes, or monkeys and apes, while at other times it's drawn from data on all primates. Sometimes it focuses on relative size of necortex and sometimes on overall brain size. They also noticed that each time Dunbar suggests a new approach for calculating the number, the values change. As the Swedish team put it: "This creates a situation where every new suggestion also produces a new, different 'Dunbar’s number'."
I agree that varying estimates of Dunbar's number is a problem, especially because the definition of what the number refers to is squishy. That squishiness allows researchers to adjust the definition of "friends", or whatever, every time they get a new estimate of Dunbar's number. In other words, once they choose which species and what aspect of the brain to include in their analyses, they can generate a number and then adjust their definition of a stable social group so that it matches the number.
Ultimately, the problem with Dunbar's number is that we don't have a precise, agreed-upon way of measuring any of the key variables. Should the dataset include all primates, or just those most closely related to humans? Should the brain measures focus on relative volume of neocortex, relative density, or something else? What exactly are the "friends," or "meaningful social groups" that are being counted?
I won't accuse Dunbar of fishing, but at this point, with so much flexibility in how the key variables are defined, any further work on clarifying Dunbar's number would amount to exactly that. As the Swedish team demonstrated in a separate paper, when you describe the evolution of the primate brain, there are so many anatomical variables to choose from that you could always find one that predicts another variable of interest (e.g., social group size).
What we're looking at here is known as the problem of "spurious relationships" or "spurious correlations". If you run enough analyses and/or cherrypick the variables used in your analyses, you're bound to find some significant relationships by chance, even though the the variables aren't related. For example, check out the graph below showing that from 2000 to 2009, the divorce rate in Maine was almost perfectly correlated with per capita consumption of margarine across the US.
Obviously, this near-perfect correlation (.99) doesn't mean that the variables are truly related. It shows up because the researchers ran over 95,000 separate correlations (!), and with that many analyses, flukes are likely to occur. (So, if you're married, and both of you prefer butter, no worries.)
I'll close with two suggestions:
1. Don't rule out some version of Dunbar's number.
Although I've picked on Dunbar's number, my point is merely that there's currently zero persuasive evidence for it. In the future we may discover that such a number does exist. My opinion is that if it does, it will vary from person to person, because people differ in their social skills, their motivation to maintain friendships, the amount of leisure time they have to pursue friendships, and so on.
2. Beware of magical numbers.
In a previous newsletter, I noted that the 10,000-steps-per-day recommendation originates in a brand name rather than in science, and I summarized evidence against the principle that 10,000 hours of practice leads to expertise. In the future, I'll look at other "magical" numbers, such as the the 4-second workout that made the news this month.
Clearly, some numbers tell us about what it means to be human. We have 2 eyes, 2 sex chromosomes, and an ability to run marathons with a lower limit of about 2 hours. (Although this particular number may diminish in the future, it's not likely to change much, because it reflects numerous constraints on human physiology.)
At the same time, not everything about us can be counted, as this newsletter illustrates. Dunbar's number would be useful if it existed, but there’s no solid evidence yet that it does.
Thanks for reading, friends!