Some fascinating figures from Spain where gay marriage has been legal since 2005, fromÂ the latest Affinity bulletin.

The table shows the number of same-sex and other sex marriages from 2000 onwards. 2005 was the year that gay marriage was introduced (mid-year).

Year |
Same-Sex Marriages |
Other-Sex Marriages |

2000 | 194,022 | |

2001 | 201,579 | |

2002 | 203,453 | |

2003 | 208,146 | |

2004 | 216,149 | |

2005 | 1,275 | 211,025 |

2006 | 4,574 | 207,244 |

2007 | 3,250 | 200,447 |

2008 | 3,549 | 193,064 |

2009 | 3,412 | 172,540 |

2010 | 3,583 | 167,232 |

2011 | 3,880 | 159,205 |

Now, just looking at the figures itâ€™s very clear that the number of other-sex marriages drops dramatically after 2005, but we know enough about stats here to realise that what we need to do is to qualify whether that is a significant drop or not. The way we do that is to build two quick models â€“ one for the figures from 2000 to 2004 and one for 2006 to 2011. Using those two models we can see if there is a significant difference between the two rates in the two periods being compared. Remember, â€œsignificantâ€ means that we are at least 95% certain that the trends we are looking at are real and not just random.

So, the two models. Firstly the 2000 to 2004 model.

Year Coefficient | 5082.1 |

P-Value | 0.003084 |

Upper 95% Bound | 6918 |

Lower 95% Bound | 3245 |

Letâ€™s explain that. A simple regression shows that the line of best fit has a coefficient of 5,082. This means that during the period 2000 to 2004,Â **on average**Â the number of other-sex marriages increased by 5,082 per year. We are 95% certain that the true value of the long term trend is somewhere between 3,245 and 6,918 which tells us that we are pretty well certain that there was an upward annual trend in other-sex marriages during those years.

Itâ€™s worth pointing out that we can assess the 95% certainty from the P-value. If this is less than or equal to 0.05 (i.e. 95%) then we say that the coefficient is significant. If the p-value had been 0.05 the lower 95% bound would have been 0.

Right, now the 2006 to 2011 model (we leave 2005 out because it is the year of transition with same-sex marriages from July onwards).

Year Coefficient | -10296.1 |

P-Value | 0.000397 |

Upper 95% Bound | -7682 |

Lower 95% Bound | -12910 |

You can probably work out whatâ€™s going on. Our coefficient is now -10,296 telling us thatÂ **on average**Â the number of other-sex marriages dropped by that amount every year. The upper and lower values of the 95% significance bounds indicate that this is a certain downward trend. Other-sex marriages have definitely been dropping year on year since the introduction of same-sex marriage.

What we can be certain of is that since the introduction of same-sex marriage the rate of other-sex marriage in Spain changed from a clear growth rate to a clear declining rate. Although the golden rule is that correlation does not equal causation, itâ€™s pretty clear that there is a direct link between the two events. Letâ€™s see if we can prove it statistically.

I thought first that it might be interesting to see if there was a direct link to the number of same-sex marriages and the number of other-sex marriages. I ran another regression on the 2006 to 2011 dataset, bringing in YearÂ **and**Â same-sex marriage numbers as predictors of other-sex marriages.

Year Coefficient | -10372 |

Year P-Value | 0.00271 |

Same-Sex Marriage Coefficient | -1.026 |

Same-Sex Marriage P-Value | 0.832 |

Once again Year gives us a significant coefficient. Same-Sex Marriage numbers give us a negative coefficient of -1.026 (indicating that for every same-sex marriage there is a reduction of one in the number of other-sex marriages) but the P-Value is 0.832, way way higher than 0.05. Because of this we reject the idea that the number of same-sex marriages in a particular year affects the number of other-sex marriages. For the record I also ran this regression as a step-wise to see if the numbers of same-sex marriages added any significant information once the year coefficient was calculated â€“ the result was negative.

What about demonstrating a straightforward link between the introduction of same-sex marriage and the annual change in other-sex marriages? I looked at regressing the Year and the presence or otherwise (as a dummy) of same-sex marriage against the annual change in other-sex marriages. The table of that data is below.

Year |
Same-Sex Marriage? |
Change in Other-Sex Marriages |

2001 | No | +7,557 |

2002 | No | +1,874 |

2003 | No | +4,693 |

2004 | No | +8.003 |

2007 | Yes | -6,797 |

2008 | Yes | -7,383 |

2009 | Yes | -20,524 |

2010 | Yes | -5,308 |

2011 | Yes | -8,027 |

The results of a step-wise regression are very interesting. The first variable that comes in is the Same-Sex marriage dummy.

Dummy Coefficient | -15,139 |

P-Value | 0.0029 |

This tells us that the presence of same-sex marriage in any year, regardless of the year, reduces the change in other-sex marriages by over -15,000. Thatâ€™s easily enough to move from growth to decline. We are 99.7% confident this is a real effect. When we then try to enter in the year itself we donâ€™t get a significant p-value. This means that we**Â reject**Â the hypothesis that there is a change in the number of other-sex marriages that is a general trend over time. Put simply, this means that the annual change is connected to the introduction of same-sex marriage and NOT a general long-term trend (as some have argued elsewhere).

So, what can we say from this? We are pretty certain that there are two different patterns in other-sex marriages registered in Spain pre and post the introduction of same-sex marriage. Â Those patterns seem to be directly linked to the introduction of same-sex marriage and are not part of a general trend in the time period we have data for. Whether one causes the other is of course a matter for further research.

A word of caution â€“ it would be interesting to add pre-2001 marriage data into the mix to see if the final analysis (regressing against year and a dummy for same-sex marriage) holds up in a longer time period. Furthermore, given that Spain is a very religious county (Roman Catholic), one cannot automatically assume that such aÂ phenomenon would repeat itself here in the UK. Indeed, if someone could supply me with the data from some of the other countries in Europe that have already introduced same-sex marriage, we could test that hypothesis.

Thoughts?

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