# Explain this statistical statement (article on marriage rates)

So, I’m reading this article on marriage rates and inequality, and I came across the following statement:

I don’t get it. How can couples in a given population have longer marriages than those outside if the population has a higher divorce rate? Is this just Simpson’s Paradox? Are the two parts of the statement not considering the same populations? Is there some other effect that’s causing secular couples to have shorter marriages, but a lower divorce rate?

Can someone explain how this works to me, possibly with some example populations that exhibit this statistical quirk?

If one group dies quickly, you could do this.

Let’s say you had a 3 person religious community, one woman and two men, where the woman marries one man for 30 years, divorces, marries the other man for 20 years, and then divorces, for a divorce rate of 100% and an average marriage length of 25 years.

Let’s say there was a secular religious community with two people, a gay couple. They get married and then one of them gets eaten by a tiger 5 years later. That gives a divorce rate of 0% and an average marriage of 5 years.

Of course, this was an easy example to construct because I used an extremely small sample size. I’d be curious to look at the distributions they showed for length of marriage and reason for marriage ending.

You have to follow the linked articles,which appear to distinguish between religious couples vs people who live in religious areas, whether they themselves are religious:

Another extreme example. Say everyone gets married at the same time and dies 50 years later.

-Mormons could all get divorced on their deathbeds (50 year average marriage, 100% divorce rate)
-Half of non-Mormons could get divorced in first year (~25 year average marriage, 50% divorce rate)

I did read the linked article, but the sentence I quoted doesn’t seem to allow that interpretation, since it says: “couples embedded in a religious community (such as the Mormons in Utah) have marriages that last somewhat longer than those who do not attend church at all”. That is, it’s contrasting “couples embedded in a religious community” with “those who do not attend church at all”.

I suppose this could just be blatant lying with statistics by appearing to contrast two non-overlapping subsets of the population, but actually doing something really weird and considering the subset of where people live for one measure and their church attendance for another. If so, I should just ignore the article since it’s intellectually dishonest.

After thinking more, I think it might be this: The divorce rate is the rate per 1000 people, not per 1000 marriages. So, if a population has a much higher rate of marriage, it could have a higher rate of divorce and a longer average marriage length, even if all else is equal.

Example:
Population A has 20% of people get married, 1/4 of whom get divorced after an average of 10 years, and the rest stay married until death for an average of 40 years, which gives an average marriage length of 32.5 years and a divorce rate of 5%.

Population B has 80% of people get married, 1/10 of whom get divorced after an average of 10 years, and the rest stay married until death for an average of 40 years. That gives an average marriage length of 37 years, and a divorce rate of 8%.

Or the fairly obvious: religious people get married at an earlier age.

One other point (at least, I didn’t see it mentioned in the comments so far): non-religious people get married later in life than religious people. So they get a 10 year head start (married at 18 instead of 28), and by the time they divorce, they’ve been married longer. If the divorce rates are close, then the extra ten years at the time of divorce could make the difference.

Suppose everyone lives to 78, and all religious people marry at 18, non-religious at 28, and the religious divorce rate is 50%, non-religious is 40%. Everyone who divorces divorces at age 43.

10 Religious couples have 5 divorces at age 43, giving them 525 + 560 years of marriage = 425 years of marriage, or 42.5 per marriage on average.

10 non-religious couples have 4 divorces at age 43, giving them 415 + 650 years of marriage = 360 years of marriage, or 36 per marriage on average.

I don’t follow the OP. This is the obvious answer and the one I assumed was meant by the quote. Perhaps the OP is thinking about the average length of marriages?

And it doesn’t have to be earlier marriages, it could simply be later divorces. Either way, more religious folks marry and subsequently divorce than non-religious folks.

The linked article links to another article which is about the correlation of divorce and religious regions. It means communities to mean geographic areas and not groups of like minded people. It concludes that in areas where religiosity is high, there is a norm of early marriage and early childbirth. This affects the non-religious as well and the non-religious end up marrying earlier than the norm for the country as a whole and subsequently divorcing at a higher rate. The religious themselves, marry early but do not have the higher divorce rate.
From looking at his data, it might be that this is Simpsons paradox because of the different racial mixes in various areas.

Both group A and Group B contain 100 people.

In Group A, 20 people get married, with the average marriage lasting 10 years before ending in divorce.
In Group B, 80 people get married, with the average marriage lasting 15 years before ending in divorce.

In both groups, 100% of marriages end in divorce, but in Group A there are 10 divorces per 100 people while in Group B there are 40.

The Church of Latter Day Saints (what “the Mormons” prefer to be called), IIRC, strongly encourage marriage. Most members will be married by 21, so I would expect a predominately Mormon community to have nearly a 100% marriage rate. I believe the Church also discourages divorce, so somebody who made a mistake in choosing a mate will be feeling social pressure to stay married.

So let’s look at 2 more hypothetical groups:
Group C has a marriage rate around 50%, with 50% of those ending in divorce in an average of 10 years.
Group D has a marriage rate of 95%, with 60% of those ending in divorce in an average of 15 years.

It’s a little hard to argue with Group D pushing for marriage so hard, since 38% of their members are presumably “happily married” in that they never got divorced, compared with just 25% in Group C. On the other hand, 57% of their members weren’t happy in their marriage (compared with 25% in Group C), and it took them on average 5 more years to conclude they couldn’t take it any more and they wanted a divorce even if it caused friction with the church. And that makes one think there are also unhappy people who decide, however unhappy they are, they’d be less happy with the social stigma of being divorced.

I wonder what the statistics are for couples who are married, but live separately?

I don’t think this is particularly intellectually dishonest, but it isn’t especially clear writing and it certainly isn’t well cited.

There appear to be two general findings reported in the sentence in question. First, couples embedded in a religious community have longer marriages (i.e., lower likelihood of divorce). “Embedded in a religious community” isn’t exactly a precise definition, but thisreview article summarizes that the risk of divorce is lower when couples attend church together with higher frequency, or when wives attend church more frequently than husbands. Conversely, in couples where the husband attends church more frequently than the wife, the risk of divorce is higher. In general, this part of the confusing sentence is comparing married couples to other married couples and looking at variation in church attendance.

The second part of the sentence actually provides a cite. This study looked at divorce rates by county in the US and focused on the variation in the concentration of conservative or evangelical protestants in each county. Counties with more conservative/evangelical protestants have higher divorce rates. (The authors say that higher concentrations of conservative/evangelical protestants are associated with abstinence-only education, more trouble finding birth control or abortion, general distrust of secular education, and general expectations of early marriage and childbearing. Young marriage, young childbearing, poor education, and crappy job market positions are all associated with increased rates of divorce in the U.S.) Anyway, this part of the sentence is comparing divorces per person per year across geographical areas.

Bottom line, the writing should be clearer. But it is an interesting intellectual puzzle.

Actually, the most obvious answer is that religious people marry more frequently. You can have longer-lasting marriages that end in divorce more if there are more of them.