Nov 17, 2013

# XL-Files: Romantic Regression towards the Mean

Contributing Editor Xiao-Li Meng recently officiated at the wedding of two young colleagues. He writes:

The International Year of Statistics seems to have brought me some unusually exciting, and challenging, speaking opportunities. The last XL-Files documented my 24 second Ig Nobel fame, which came with the grand challenge of explaining statistics clearly to a lay audience in seven words. Another equally unique and nerve-wracking experience came only a few weeks later. This time I was asked to officiate a wedding of two members of my Happy Team.

Are you kidding me? A statistician officiating a wedding? Well, read on, especially if you have no one to kid around with tonight, or must sleep in your study where my XL-Files await.

Opening Remarks at the wedding of Victoria and Yves:
Ladies and Gentlemen, almost all wedding ceremonies are conducted in one universal language, Love. But Victoria and Yves are so special that today we will employ two universal languages to celebrate their wedding: Love and Statistics. Please be seated, especially if the very mention of statistics makes you dizzy.

Let me start by asking a simple question: What are the chances that two statisticians fall in love with each other, during a course entitled “Real-life Statistics: Your Chance for Happiness (or Misery)” , which started with a module on Romance? If you find that question too difficult, let’s try this one: What’s the connection between Statistics and Romance?

The answer is soulmate. Have you found yours? If not, there are plenty of online sites that promise to find one for you, if you are willing to fill out a questionnaire and make a sizeable donation. But what is their magic formula? Well, the answers you provide about your lovely self and your loving desire will be fed into a formula called Romantic Regression, a term I was told was coined by someone in another school in Cambridge too small to have a statistics department. This magic formula, which is known to statisticians as Logistic Regression, will then seek another lost soul with the highest matching probability to yours.

Being top statistics students in the right school in Cambridge, who were also too poor to make a sizeable donation, Yves and Victoria knew a better way to find their soulmates. Instead of relying on any magic formula, they found that magical feeling in each other’s hearts by joining the team that designed and taught the aforementioned happy course. Being a not too shabby statistician myself, I can give you a 99% confidence interval on when, and where, that magical moment took place. It was between July 12 and 22, 2010, on the Fudan campus in Shanghai, where Yves and I were co-teaching a version of the happy course for a study abroad program. I had also invited Victoria and a few other members of the Happy Team to join us for a short period.

Harvard professors do not have access to their teaching fellows’ email boxes. But I had my data, all observational, nevertheless signaling. Since statisticians make a living by extracting signals from noisy data, please allow me to demonstrate how I turned my very limited data into a heartwarming discovery. Along the way, I hope I can make statistics less (or more) dizzying for you.

Data Point One: Being an extremely well-mannered and courteous young man, Yves had always responded to my inquiries and requests in the most pleasant and helpful way. However, somewhere during that ten days when I asked Yves if another Happy Team member could join an excursion Yves and Victoria had already planned, Yves’ answer was as dazzling as his tango moves, starting from the difficulty of getting train tickets, to uncertainty about where they would actually visit, to whether they would return the same evening. Statistical Lesson One: A statistically significant test is the one where the data are in serious contradiction to the hypothesis that nothing is going on.

Data Point Two: Before their excursion, only Yves had the flu. After they returned, Victoria was so sick that she lost her voice. Statistical Lesson Two: Although association does not imply causation, it is often a good first step to build evidence, especially when the time direction is consistent with the causal direction.

Data Point Three: On August 15, 2010, Victoria wrote to me: “I thank you from the bottom of my heart for the trip to Shanghai. Believe it or not, it actually changed my life in more than one way … It was truly unbelievable and unforgettable.” Statistical Lesson Three: Good data can speak for themselves.

Alright, enough advice on statistics. Time for advice on marriage, as Victoria and Yves have asked me to provide. Advice about marriage from a statistician? Yes, because statisticians understand well the universal law of regression towards the mean. In layperson’s terms, it simply means that if you are at the top, then there is only one direction to go. Most of those who have ever chased high-return stocks can give personal and painful testimony about this fact. Statistically speaking, when two people fall in love to the degree that they decide on marriage, their expectations of each other, and indeed of themselves, are extremely high. Some of these expectations are reflections of reality and hence sustainable. But others are idealizations, or what we statisticians would call a model. But nobody can be a model 24/7, not even a super-model.

Clearly the only logical conclusion is that statisticians should be among the most desirable soulmates. Yves and Victoria obviously understand that simple fact, which is why I signed Yves’ PhD thesis in statistics as a member of his thesis committee, and I officially presented Victoria her PhD degree in statistics as the dean of the graduate school. I am therefore extremely happy and very grateful that today I have the opportunity to present them with a joint PhD: Perfectly Happy Devotion to each other.

Exchange of Rings:
A ring is a perfect symbol of regression towards the mean, because whereas any ring is expected to be a perfect circle mathematically, a closer inspection would almost always reveal some charming individualities. It therefore symbolizes our common desire for perfect love, but it also reminds us that to love perfectly, we must accept each other for who we are.

Closing Remarks:
Victoria and Yves, it has been a true privilege for me to have both of you as my students and dear friends, and I am certain that all your family members, friends, and colleagues feel the same joy to have you as a part of their lives. Now you are just a few minutes away from officially being in each others’ lives for good. Everybody, here and elsewhere, will expect your marriage to be as perfect as marriage can be, and I am as confident as a statistician can be that you will defy the law of regression towards the mean.

But before I proceed with the formal declaration of marriage, Yves, I’d like to tell you what I expect from you. Yves, as you know, at the end of the declaration, I will give you permission to kiss the bride. Of course both of us know well that you do not need my or anyone else’s permission to kiss Victoria—after all, I suspect that was how you made her voiceless in China. But this time I expect you will gather all your charm and strength, to give her the kiss of her life and your life. That is, instead of making her voiceless, make her breathless and speechless. Can you deliver that?

In case you wonder whether I delivered what Victoria and Yves had expected from me, may I brag that now I have a non-empty client base for those who want “a funny, personal, and intellectually engaging wedding ceremony”? I never brag without data—during the Russian-style wedding feast, a couple approached me: “If we were not married, we definitely would have hired you!”
Are you married?

We made this Tagxedo from the “Glossary of Statistical Terms” at www.stat.berkeley.edu/~stark/SticiGui/Text/gloss.htm. Make your own statistical Tagxedos and share them at our Facebook page, https://www.facebook.com/IMSTATI

• Professor Meng, we have a mutual friend, Charlie Shi. That’s a bravo speech, I wish I had it for reference at my eldest daughter’s wedding. It will surely have a bearing on my speech at my second daughter’s. The data signal you have a happy marriage Prof. Meng. It is probable through Charlie’s kind arrangement, I will have the pleasure of meeting you one day.

• […] my happy course ultimately led to a happy wedding [in Harvard’s Memorial Church—described in XL-Files in the December 2013 issue]. Yes, that took place on October 5, 2013, and if you check the Memorial Church’s log book, you […]

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