I took the above headline from a news article in the (London) Independent by Jeremy Laurance reporting a study by Jan-Emmanuel De Neve, James Fowler, and Bruno Frey that reportedly just appeared in the Journal of Human Genetics.

One of the pleasures of blogging is that I can go beyond the usual journalistic approaches to such a story: (a) puffing it, (b) debunking it, (c) reporting it completely flatly. Even convex combinations of (a), (b), (c) do not allow what I’d like to do, which is to explore the claims and follow wherever my exploration takes me. (And one of the pleasures of building my own audience is that I don’t need to endlessly explain background detail as was needed on a general-public site such as 538.)

OK, back to the genetic secret of a happy life. Or, in the words the authors of the study, a gene that “explains less than one percent of the variation in life satisfaction.”

“The genetic secret” or “less than one percent of the variation”?

Perhaps the secret of a happy life is in that one percent??

I can’t find a link to the journal article which appears based on the listing on De Neve’s webpage to be single-authored, but I did find this Googledocs link to a technical report from January 2010 that seems to have all the content. Regular readers of this blog will be familiar with earlier interesting research of Fowler and Frey working separately; I had no idea that they have been collaborating.

De Neve et al. took responses to a question on life satisfaction from a survey that was linked to genetic samples. They looked at a gene called 5HTT which, according to their literature review, has been believed to be associated with happy feelings.

I haven’t taken a biology class since 9th grade, so I’ll give a simplified version of the genetics. You can have either 0, 1, or 2 alleles of the gene in question. Of the people in the sample, 20% have 0 alleles, 45% have 1 allele, and 35% have 2. The more alleles you have, the happier you’ll be (on average): The percentage of respondents describing themselves as “very satisfied” with their lives is 37% for people with 0 alleles, 38% for those with one allele, and 41% for those with two alleles.

The key comparison here comes from the two extremes: 2 alleles vs. 0. People with 2 alleles are 4 percentage points (more precisely, 3.6 percentage points) more likely to report themselves as very satisfied with their lives. The standard error of this difference in proportions is sqrt(.41*(1-.41)/862+.37*(1-.37)/509) = 0.027, so the difference is not statistically significant at a conventional level.

But in their abstract, De Neve et al. reported the following:

Having one or two allleles . . . raises the average likelihood of being very satisfied with one’s life by 8.5% and 17.3%, respectively?

How did they get from a non-significant difference of 4% (I can’t bring myself to write “3.6%” given my aversion to fractional percentage points) to a statistically significant 17.3%?

A few numbers that I can’t figure out at all!

Here’s the summary from Stephen Adams, medical correspondent of the Daily Telegraph:

The researchers found that 69 per cent of people who had two copies of the gene said they were either satisfied (34) or very satisfied (35) with their life as a whole.

But among those who had no copy of the gene, the proportion who gave either of these answers was only 38 per cent (19 per cent ‘very satisfied’ and 19 per cent ‘satisfied’).

This leaves me even more confused! According to the table on page 21 of the De Neve et al. article, 46% of people who had two copies of the gene described themselves as satisfied and 41% described themselves as very satisfied. The corresponding percentages for those with no copies were 44% and 37%.

I suppose the most likely explanation is that Stephen Adams just made a mistake, but it’s no ordinary confusion because his numbers are so specific. Then again, I could just be missing something big here. I’ll email Fowler for clarification but I’ll post this for now so you loyal blog readers can see error correction (of one sort or another) in real time.

Where did the 17% come from?

OK, so setting Stephen Adams aside, how can we get from a non-significant 4% to a significant 17%?

– My first try is to use the numerical life-satisfaction measure. Average satisfaction on a 1-5 scale is 4.09 for the 0-allele people in this sample and 4.25 for the 1-allele people, and the difference has a standard error of 0.05. Hey–a difference of 0.16 with a standard error of 0.05–that’s statistically significant! So it doesn’t seem just like a fluctuation in the data.

– The main analysis of De Neve et al., reported in their Table 1, appears to be a least-squares regression of well-being (on that 1-5) scale, using the number of alleles as a predictor and also throwing in some controls for ethnicity, sex, age, and some other variables. They include error terms for individuals and families but don’t seem to report the relative sizes of the errors. In any case, the controls don’t seem to do much. Their basic result (Model 1, not controlling for variables such as marital status which might be considered as intermediate outcomes of the gene) yields a coefficient estimate of 0.06.

They then write, “we summarize the results for 5HTT by simulating first differences from the coefficient covariance matrix of Model 1. Holding all else constant and changing the 5HTT gene of all subjects from zero to one long allele would increase the reporting of being very satisfied with one’s life in this population by about 8.5%.” Huh? I completely don’t understand this. It looks to me that the analyses in Table 1 are regressions on the 1-5 scale. So how can they transfer these to claims about “the reporting of being very satisfied”? Also, if it’s just least squares, why do they need to work with the covariance matrix? Why can’t they just look at the coefficient itself?

– They report (in Table 5) that whites have higher life satisfaction responses than blacks but lower numbers of alleles, on average. So controlling for ethnicity should increase the coefficient. I still can’t see it going all the way from 4% to 17%. But maybe this is just a poverty of my intuition.

– OK, I’m still confused and have no idea where the 17% could be coming from. All I can think of is that the difference between 0 alleles and 2 alleles corresponds to an average difference of 0.16 in happiness on that 1-5 scale. And 0.16 is practically 17%, so maybe when you control for things the number jumps around a bit. Perhaps the result of their “first difference” calculations was somehow to carry that 0.16 or 0.17 and attribute it to the “very satisfied” category?

1% of variance explained

One more thing . . . that 1% quote. Remember? “the 5HTT gene explains less than one percent of the variation in life satisfaction.” This is from page 14 of the De Neve, Fowler, and Frey article. 1%? How can we understand this?

Let’s do a quick variance calculation:

– Mean and sd of life satisfaction responses (on the 1-5 scale) among people with 0 alleles: 4.09 and 0.8
– Mean and sd of life satisfaction responses (on the 1-5 scale) among people with 2 alleles: 4.25 and 0.8
– The difference is 0.16 so the explained variance is (0.16/2)^2 = 0.08^2
– Finally, R-squared is explained variance divided by total variance: (0.08/0.8)^2 = 0.01.

A difference of 0.16 on a 1-5 scale ain’t nothing (it’s approximately the same as the average difference in life satisfaction, comparing whites and blacks), especially given that most people are in the 4 and 5 categories. But it only represents 1% of the variance in the data. It’s hard for me to hold these two facts in my head at the same time. The quick answer is that the denominator of the R-squared–the 0.8–contains lots of individual variation, including variation in the survey response. Still, 1% is such a small number. No surprise it didn’t make it into the newspaper headline . . .

Here’s another story of R-squared = 1%. Consider a 0/1 outcome with about half the people in each category. For.example, half the people with some disease die in a year and half live. Now suppose there’s a treatment that increases survival rate from 50% to 60%. The unexplained sd is 0.5 and the explained sd is 0.05, hence R-squared is, again, 0.01.

Summary (for now):

I don’t know where the 17% came from. I’ll email James Fowler and see what he says. I’m also wondering about that Daily Telegraph article but it’s usually not so easy to reach newspaper journalists so I’ll let that one go for now.

P.S. According to his website, Fowler was named the most original thinker of the year by The McLaughlin Group. On the other hand, our sister blog won an award by the same organization that honored Peggy Noonan. So I’d call that a tie!

P.P.S. Their data come from the National Survey of Adolescent Health, which for some reason is officially called “Add Health.” Shouldn’t that be “Ad Health” or maybe “Ado Health”? I’m confused where the extra “d” is coming from.

P.P.P.S. De Neve et al. note that the survey did not actually ask about happiness, only about life satisfaction. We all know people who appear satisfied with their lives but don’t seem so happy, but the presumption is that, in general, things associated with more life satisfaction are also associated with happiness. The authors also remark upon the limitations using a sample of adolescents to study life satisfaction. Not their fault–as is appropriate, they use the data they have and then discuss the limitations of their analysis.

P.P.P.P.S. De Neve and Fowler have a related paper with a nice direct title, “The MAOA Gene Predicts Credit Card Debt.” This one, also from Add Health, reports: “Having one or both MAOA alleles of the low efficiency type raises the average likelihood of having credit card debt by 14%.” For some reason I was having difficulty downloading the pdf file (sorry, I have a Windows machine!) so I don’t know how to interpret the 14%. I don’t know if they’ve looked at credit card debt and life satisfaction together. Being in debt seems unsatisfying; on the other hand you could go in debt to buy things that give you satisfaction, so it’s not clear to me what to expect here.

P.P.P.P.P.S. I’m glad Don Rubin didn’t read the above-linked article. Footnote 9 would probably make him barf.

P.P.P.P.P.P.S. Just to be clear: The above is not intended to be a “debunking” of the research of De Neve, Fowler, and Frey. It’s certainly plausible that this gene could be linked to reported life satisfaction (maybe, for example, it influences the way that people respond to survey questions). I’m just trying to figure out what’s going on, and, as a statistician, it’s natural for me to start with the numbers.

P.^7S. James Fowler explains some of the confusion in a long comment.