So, apparently, being married is good for you. Married, I tells ya, as in party to a matrimonial contractual arrangement with a legally eligible spouse. Why might this be? Well, one advantage to being married is that your tax and inheritance provisions tend to be facilitated by legislation in ways that materially advantage you over non-married folk. And if you are inclined toward such stuff, you may also expect your relationship will be spiritually blessed by whatever deity you think morally underwrites your existence.

But what you mightn’t count on are the associated medical benefits. And quite specific ones at that. Because, according to several media reports this week, scientists have now revealed that “being married” makes you twice as likely to be alive 15 years after heart surgery. Or three times as likely, if you read a different media website. Or four times as likely if you read another. Whichever, it seems like quite a lot. Put the other way around, it means that not being married makes you only half, a third, or a quarter as likely to survive as someone who has been wedded in holy (or civil) matrimony.

It was a pretty simple message; so simple, in fact, that the media ended up gravitating toward a relatively narrow repertoire of similarly worded headlines. The LA Times went with “Marriage helps the heart“, while CBS News had “Marriage tied to longer survival after heart bypass“. Both USA Today and CNN came up with “Marriage helps survival after heart surgery“. Meanwhile, some of the more socially conservative outlets emphasized the importance of having a cohesive marriage: “Take Heart! A good marriage protects even after a bypass” proclaimed Fox News; while the Christian Post declared that “Healthy marriages lead to healthy hearts“. And these pronouncements were not intended as social value-statements moderated by conservative editorial stances. No, science told us that all this is so, apparently.

Except it didn’t, of course.

The study referred to in all these news reports has just been accepted for publication in the academic journal Health Psychology, and is scheduled to appear in a forthcoming issue (subscribers can download an advance copy from the journal’s website). Conducted by researchers at Rochester University, New York, the methods were simple and direct. A group of 225 heart bypass patients who underwent surgery between 1987 and 1990 were followed up 15 years later. Patients who were married were 2.5 times more likely to be alive at follow-up. The researchers also circulated questionnaires the year after surgery. These showed that patients who rated themselves as being more satisfied with their marriages were statistically more likely to survive the subsequent 14 years. All very interesting. But while this was a strong study with unique longitudinal data and clinically relevant outcome measures, things weren’t quite as simple as portrayed in the mass media.

The researchers present much of their data in the form of percentages with sentences like this:

The survival plot in Figure 1 shows that 61.3% of the married group was alive after 15 years, whereas only 29.5% of the not-married group was alive.

The good thing about using percentages is that imbalances in the numbers of “married” and “non-married” patients overall can be put aside in order that differences in survival rates can be emphasized. However, one unfortunate consequence is that the underlying figures can sometimes be more informative. While “61.3%” certainly seems far higher than “29.5%“, the actual figures represented by such percentages are far less convincing. This is because the group-sizes were rather uneven: of the sample of 225 patients, the vast majority (80.4%) were in the “married” category.

As a result, after you do the necessary computations (i.e., “61.3% of 80.4% of 225” and “29.5% of 19.6% of 225”) this is what the underlying data actually look like:

Now at first glance, we see that 111 “married” patients survived, which is far more than the 13 “not married” patients who survived. Then again, far more “married” people died as well, because, simply, far more patients were married overall. So it certainly makes sense for the researchers to focus on percentages.

However, consider for a moment the percentage difference in real-number terms. One way to do this is to take the survival rate for “married” patients and apply it to the “not married” patients. In other words, seeing as 61.3% of “married” patients survived, what would this survival rate look like had it occurred among “not married” patients? Well, had that been the case, then a total of 27 “not married” patients (i.e., 61.3% of 44) would have been alive at follow-up. In other words, only 14 additional patients would have survived, which might not seem like a lot.

But we also need to take account of statistical significance. The reason the current findings are reported in an academic journal is not because the survival rate among married patients was simply higher than among unmarried patients, it was because it was statistically significantly higher. This means (roughly speaking) that the likelihood of the difference occurring by chance alone was less than 1-in-20 (or a within a probability level, or p-value, of 0.05, the conventional threshold agreed by statisticians as representing a reasonable cut-off between flukes and non-flukes).

The point here is that survival rates can differ due to pure chance alone, such as when you get 6 heads and 4 tails from 10 coin tosses. So a question we can ask is: what survival rate among “not married” patients would have produced a finding of “no significant difference”? 

Well, the answer is this:

Here, the difference in survival rates between “married” and “not married” participants is not statistically significant (in fact, based on a chi-squared test, the p-value is 0.0623). But compared to reality, only 7 additional “not married” patients survive in this (hypothetical) scenario.

In other words, the difference between the Rochester study and one that would have been ignored by the world’s media was just seven people.

As well as being “not married”, these seven people are likely to have differed from their (surviving) married counterparts in lots of other ways. For example, maybe they smoked more. Notably, when the researchers included smoking in their statistical analyses, the difference in survival rates lost their “statistically significant” status. And maybe heavy smokers are less likely to get married in the first place. In other words, maybe being “unmarried” is not one of the causes of poor health, but one of its consequences.

The findings relating to the “marriage satisfaction” ratings were also problematic. For one thing, no other type of satisfaction was measured. Thus, patients who were dissatisfied with their marriages may also have been dissatisfied with everything in their lives. Again, it is notable that when the researchers included depression as a variable in their analyses, the difference between the two survival rates disappeared once more. (What the researchers really needed here was not a measure of marriage-satisfaction on its own, but rather a measure of marriage-satisfaction-relative-to-satisfaction-with-life-in-general.)

And one final problem, which relates especially to how the study was reported in the media, is something of an elephant in the matrimonial bedroom. It concerns the meaning of the terms “married” and “not married” in this study. Here is the researchers’ explanation:

Marital status was assessed at the time of surgery; 181 (80.4%) participants were married. Individuals who were widowed, separated, divorced, or single were included in the “not married” group [emphasis added].

Pay particular attention to the phrase “or single” in this explanation. Essentially, if people who consider themselves “single” were categorized as “not married”, then what about non-single patients who were in adult relationships but not married in the legal sense? It turns out these were included in the “married” category, on the grounds that their relationships constituted informal or common law marriages. In other words, walking up the aisle and taking public vows had nothing to do with it.

So all those news stories — and the visual images used to illustrate them — were incorrect. The whole business of nuptials, weddings, tying the knot, exchanging vows, jumping the broom, getting hitched, and partaking of holy matrimony has no effect on survival rates following heart surgery.

What the research showed was that having access to a loving, stable, and (presumably) sexual relationship with an intimate partner might — just might — be a factor in determining survival following heart surgery. Even then, the effect is reliant on the deaths of just seven unfortunate patients (from a sample of 225) across a fifteen-year period. And it only stands if you hold all other things equal. Which of course you can’t.

I wouldn’t be contacting the pastor just yet…