No Other Explanation

Readers will recall in “Reemergence of Marriage” I showed a distinct deceleration in the rate of increase in the non-marital birth ratio (ROI-NMBR)^[1] which occurred in conjunction with the American debate for Same Sex Marriage. This deceleration is what one would expect to occur if Americans responded to the twin themes of responsible parenthood and long term commitment aired by advocates of same sex marriage. Borrowing the words Dr. Stanley Kurtz used to explain a similar conjunction between changes in the Dutch ROI-NMBR and the Dutch campaign for Same Sex Marriage, I observe, “The conjunction is no coincidence”.

Mr. Katz disputed my assertion that the debate over SSM influenced the American trend. Observing that my causal mechanism relied on the theme of responsible parenthood, he requested I provide evidence of this theme. Pointing out that Dr. Kurtz has devoted lots of ink to this subject, he suggested I should also devote plenty to address the possibility that other factors may have caused the noticeable transition. Finally, he requested I demonstrate the distinct transition is statistically significant and occurs at the appropriate time to support the linkage.

In my first response to Mr. Katz, I provided evidence of that advocates emphasized the important ways children benefit when their parents marry. In my second, I demonstrated the transition cannot explained by the factors Mr. Katz suggested.

In this article, I will show the data are statistically significant and the transition occurs very near the time one might expect it to. Since the transition is statistically significant, supports the causal mechanism I have suggested and cannot be explained by theories proposed by opponents of same sex marriage, I believe it is up to those who wish to argue that same sex marriage has not strengthened marriage in the US to provide a more plausible reason for the last nine years of American marital revitalization.”^[2]

The Third Criticism
I will now address the idea that the transition did not occur near the onset of the national debate for SSM. Quoting Mr. Katz:

I interpret this to mean either:

1. The deceleration in the out of wedlock birth rate occurred too late to attribute it to the Hawaii ruling in favor of same sex marriage,
2. The change in the slope I indicate is not statistically significant or
3. Both.

Whether or not Mr. Katz intended both, people who read his column may understand him to mean both.^[4] So, I believe it is important to rebut both, earnestly.^[5]

Timing: I will first address the suggestion that the change in slope occurred to late to be associated with the Hawaii Court Case.

As I stated in my first article responding to Mr. Katz, the deceleration in the NMBR, first became evident in 1995. Is this too late to attribute it to the 1993 Hawaii Court case?

At first glance it may appear so; some might overlook the 9 month gestation period for humans.^[6] So, it may surprise them to learn that some women pregnant on the day of the May 1993 court decision would not give birth until 1994. Thus, we would expect the 23 year trend in the ROI-NMBR to persist through a portion of 1994. To better illustrate these two events, I shifted the line indicating the Hawaii court ruling to suggest its May date, and added another to note the end of the 9 month gestation period. Examining the graph, we see that no matter what we postulate about the effect of the court ruling on personal behavior, one would expect the ROI-NMBR to follow the pre-Hawaii court case trend until March, 1994. View image.

One might, however, have expected a drop in the birth ratio during 1994 due to an effect during the final months. Examining the data, it appears this did not occur. Why not? There are two possible reasons:

1. There may be a data tabulation error for 1994.
2. People tend to delay; their behavior may not change instantaneously.

I consider the delay theory the more likely of the two possibilities. However, it is not possible distinguish these two based on the data I have obtained. Consequently, I will consider both possibilities, beginning with the less likely one.

To see whether the 1994 data point looks suspicious, I calculated the ROI-NMBR by subtraction.^[7] The derived values are shown in Figure 2. Note, the ROI-NMBR achieves a maximum of 1.6% in 1994 and a minimum of -0.4% in 1995; both are outliers. Examining further, the 1.6% increase in 1994, although a maximum, does not seem remarkably large. An increase of 1.5% was achieved in 1992, and increases of 1.4% had been achieved in the late 80’s. So, it is possible that the increase simply represents a continuation of the pre-Hawaii trend, and is consistent with the “delay” theory.

The 1995 minimum, however, falls well outside the ranges exhibited by both the pre or post-Hawaii data sets. It is not uncommon to suspect error when one observes distant outliers. The fact that outliers representing both a maximum and a minimum are side by side further supports the idea of error. The data shown on Figure 2 are obtained by subtraction, if one data point was erroneously tabulated or recorded, that would be the cause of the two adjacent outliers, one a maximum and one a minimum.

Figure 2: The ROI-NMBR for years 1970-2002

Since the side-by-side outliers look suspicious, it is worthwhile to consider the possibility the entry for 1994 is incorrect,^[8] particularly, in light of the “delay” theory I have yet to address. Let us assume 1994 data point is flawed, the pre-Hawaii trend in the ROI-NMBR persisted through March 1, 1994 and the post-Hawaii trend applied during the remaining months of 1994. Removing the 1994 data point, and recalculating, we would expect the cumulative two year change in the NMBR to be 1.2%.^[9] Interestingly, if we add to obtain the increase from Jan 1, 1994 (1.6%) to Dec 31, 1995 (-0.4%), we obtain 1.2%. This is exactly the value calculated assuming people responded immediately to the ruling!

The agreement is likely a complete coincidence. It is, in fact, amazing given the year to year statistical variability expected in the ROI-NMBR even during stable periods. However, if the 1994 data point is wrong, this agreement suggests the possibility that couples young and old changed their behavior very quickly after the Hawaii court ruling!

Now let us consider the more likely possibility the pre-Hawaii trend persisted because people did not change their behavior immediately. Is this plausible?

We know the Hawaii court case was reported and discussed nationally. However, just as most political discussion of the Goodridge case came after the ruling, the bulk of political discussion also came after the Hawaii ruling. In any case, some Americans might not listen to the news every evening; some might only hear of a topic, and the pro-family theme aired by advocates of SSM until after their friends mention the issue at summer barbecues, or church pancake breakfasts. So, it is possible many did not become aware of the Hawaii ruling for several months.

If people delayed their response for these reasons, it seems plausible to me the ROI-NMBR would not decelerate in 1994. The fact that the 1994 birth ratio follows the pre-Hawaii trend simply implies people persisted in their pre-Hawaii beliefs and behaviors for a number of months. However, is the explanation that American’s might not respond instantaneously plausible to others?

Possibly. It seems at least one person has postulated the tendency of people’s behavior to lag judicial rulings. In “Scandinavia by the Numbers”^[10], explaining the delay in Danish marital behavior, Mr. Katz suggests this “delay theory”:

There we have it! It takes time before people change their attitudes about marriage. Just as people don’t divorce the day after a judicial ruling, cohabiting couples might not rush to churches and marry; they might spend some time internalizing the decision before making a marital commitment. Afterwards, they might spend time planning their wedding. Other cohabiting couples who after some months of discussion decide to part might wait until their leases run out. During this transition period, some women may find themselves unintentionally pregnant. If their pre-Hawaii attitude persists, the couple may choose not to marry and these births will contribute to the 1994 out of wedlock birth statistics.

So, just as I suggested when I discussed the effect of The Welfare Reform Act, one might expect a delay of several months beyond the 9 month gestation period before the Hawaii ruling affects American’s behavior. If Americans did wait several months, 1994 data would not reflect the effect of the 1993 ruling. Instead, 1995 is the first year when one should expect to detect the effect of the Hawaii ruling on the NMBR. That is the year when the change first becomes visible in the data.

Since the transition occurred the first year when one likely expects to detect it, I think it is fair to say the transition was “almost immediate”!

Statistical significance
Mr. Katz is correct to mention I failed to show the transition in the ROI-NMBR is statistically significant.^[11] I will now remedy this deficiency.

To evaluate statistical significance, I compared the mean ROI-NMBR for the “pre-Hawaii” and “post-Hawaii” groups; these are 0.9%/year and 0.2% /year. These two values differ by a factor of 4.5. Dr. Kurtz claims a factor of 2 change in the Dutch ROI-NMBR and deems that meaningful. So, I assume a change by a factor of 4.5, which is more than twice a large, is agreed to be meaningful.

Nevertheless, the fact the difference in the two means is large does not mean the difference is statistically significant. To test for significance, I performed a two-tailed T-Test. The difference in the means to be significant to the 99.995% confidence level; this is greater than the 95% confidence level generally thought to imply statistical significance.^[12]

So, we seen the deceleration in the ROI-NMBR is strong, statistically significant, and is reflected as soon after the 1993 pro-SSM Hawaii judicial ruling as might be thought plausible.

Conclusion
I believe I have addressed Mr. Katz’s criticisms and shown that the correlation between deceleration in the ROI-NMBR and the campaign for SSM is, indeed, “very good”. The deceleration in the American out of wed lock birth rate is both large in magnitude, and statistically significant. The slight delay noted by Mr. Kats is expected because of the 9 month gestation period and the additional delay theory proposed by Mr. Katz. Because of this delay, one would expect 1995 would be first year when the birth rate might be unambiguously affected by the 1993 Hawaii ruling. That is precisely when the transition became evident, and supports my contention that the transition occurred after the Hawaii Ruling which brought the pro-family pro-commitment message of those advocating legalized same sex marriage to national attention. American’s listened and responded.

Who has the burden of proof? It is now up to the opponents of same-sex marriage to show why we should believe them when they say that same-sex marriage will weaken American marriage as a social institution. Why should we weaken the linkage between parenthood raising children by legally prohibiting some parents from marrying? Children of gay parents deserve the legal protection of parents united in marriage.

======End Notes.

[1] The rate of increase in the non-marital birth ratio is the parameter selected by Dr. Kurtz to encapsulate the health of marriage in the Netherlands. As this term is cumbersome, I will be using the acronym ROI-NMBR, which I pronounce the “roy-number”.

[2] “No Explanation” Dr. Kurtz said: “But it is up to those who wish to argue that gay marriage has not undermined marriage in the Netherlands to provide a more plausible reason for the last seven years of Dutch marital decline.”

[3] Although Dr. Kurtz also did not provide a hyper link in “Going Dutch”, and I was mimicking his style of presentation when I wrote “Reemergence of Marriage”, this particular omission was inadvertent. The data for 1970-1999 are available at the CDC. The data for 2000 and 2001 appear in the National Vital Statistics Report Vol. 51, No. 2. Published Dec 18,2002, and data for 2002 appear in NVSS Report Vol. 52 No 10, Published Dec 17, 2003.

[4] I note that Mr. Katz does not suggest my analysis suffers from the “cum hoc ergo propter hoc” fallacy which “Alas A Blog” readers perceive. For this reason, I will not address that in my responses to Mr. Katz. I will be addressing that fallacy, and its relationship to Dr. Kurtz’s and my paper after the poll I recently announced is complete. Those voting may wish to consider Matt Taylor’s recent observations published at MarriageDebate.com:

[5] While not denying the possibility of underlying irony first suggested by Mr. Katz in his criticism of my initial post, and which has been debated by Jake Squid and Don P. in the comments section of “Cause and Effect”, and “The Effect Of Welfare Reform”, I concur with Alas commenter, Don P. that my rebuttals are earnest and reflect serious intent. As Don P. points out, many of the things I say are simply true. For example: As I mentioned in my article on the theme of SSM, Andrew Sullivan really has been saying SSM will strengthen marriage and benefit children. The 1996 Welfare Reform Act really was signed in 1996.

The only way to read irony into my observation about the Welfare Reform act is to suspect that I not only knew this act existed, but that I knew it was passed in 1996, and I had considered its effect on the data. Moreover, one might need to believe I thought my readers also the bill was passed in 1996 and were sufficiently intelligent to infer that it could not cause a changes in behavior in 1994. Otherwise, how could I expect them to sense irony?

Might there be the underlying irony in earnestly addressing the flaws suggested by Mr. Katz, while failing to address the possible “Causation vs. Correlation” fallicy?

Me, use irony? As if!

[6] Let me assure readers, especially Jake Squid, I was overlooked the gestation period, lest they credit me with referring to it when I wrote: “Obviously, unmarried women already pregnant at the time of the ruling still bore their illegitimate babies. But in 1995, we see the illegitimacy rate dropped for the first time in decades.”

[7] That is: The ROI-NMBR for 2002 is obtained by subtracting the NMBR for 2001 from the NMBR for 2002. Thus it reflects the change that occurred in 2002.

[8] In fairness to the CDC and other government agencies, when I say “erroneous” I should more accurately say “less precise than usual”. Many readers may think it is trivial to determine the non-marital birth rate in any given year. However this is not as simple as it would seem. In some states, woman are asked their marital status directly and their answer is listed on the child’s birth certificate. In other states, the marital status is inferred from other information. Consequently, when state or federal workers compile the data, some imprecision is possible.

This imprecision becomes unimportant when we examine long term trends like the transition in slopes seen before and after the Hawaii ruling. However, this type of impression is very important to recognize when examining the change in the birth rate in adjacent years as we are attempting to do when interpreting the change between 1993 and 1994.

[9] I calculated prior to rounding as follows: 1.19% = 14/12 * 0.83% + 10/12* 0.26%. The factor of 14/12 assumes the pre-Hawaii trend persisted to then end of 1993 and through January and February, 1994, as might be expected since women who became pregnant on May 5th, 1993 would give birth near March 5, 1994. To account for my assumption the 1994 data point might be erroneous, I recalculated the pre-Hawaii mean ROI-NMBR, which drops from 0.89% to 0.83%. Likewise the post Hawaii mean ROI-NMBR becomes 0.26%, and for the purpose of this calculation, applies for the remaining 10 months of 1995. For discussion purposes, I rounded the final result to 1.2%.

[10] Reading this article, I learned at Mr. Katz believes we probably should not use Scandinavia to predict what might happen in the US. He warns:
“Even letting slide his [Sullivan’s] perennial attempts to use that region [Scandinavia] as a model and example in his advocacy for SSM in the United States, one can suggest that damage to the institution of marriage would only be more profoundly harmful on our shores,...”

I agree with Mr. Katz that it is dangerous to use Scandinavia to predict what will happen in the US. It is especially inappropriate when the American data are available and we can just examine them to see what already happened. The existing American data suggest that the debate for SSM has caused a deceleration in increasing out of wedlock birth rate. Dr. Kurtz argues that this is the correct parameter to use when diagnosing the health of marriage. Therefor, the data seem to suggest that the debate is benefiting marriage in the US.

[11] Although Dr. Kurtz has expended approximately 3 times as much ink as I, he has made no attempt to demonstrate the statistical significance of his data. As far as I am aware, Mr. Katz has not criticized Dr. Kurtz for this. Mr. Katz has not even lodged the rather ambiguous accusation that the Dutch “correlation isn’t that strong.” Others have.

[12] I repeated the T-test eliminating the data affected by the possible data entry error for 1994; the averages change to 0.8% and 0.3% respectively. The differences remain statistically significant. As often occurs, the confidence level actually increases when the outliers are removed..