Thursday, 8 May 2014

Statistics, Facebook, friends birthdays and coincidences

I received one of those Facebook emails the other day telling me that three of my friends had birthdays on the same day. Now this might not have been too much of a surprise to me if I had about five hundred friends, but I don’t.

Should I have been surprised given that I only have about fifty friends on Facebook ?

This is the sort of question that is all about chance: something that statisticians learn about at school or college and subsequently use in their work. But sometimes even seemingly simple questions like this can present somewhat difficult analysis for a statistician. One difficulty for us to move forward is that we have to make an assumption that all birthdays are equally likely, and clearly they are not [see box 1].

You will often see assumptions stated by statisticians, they help to describe the accuracy of conclusions that have been made from statistical analysis (

Box 1: Assumption that all birthdays are equally likely.

It turns out that there isn’t that much difference in the UK month on month. There is a peak of births in July in the UK (about 70,000 in July 2011) (, and a trough in February (about 61,000 in February 2011).

As an aside, the peak was in August in the US in 2010 (

Before trying to answer this question lets change the situation completely and consider other coincidences and chance findings we might experience socially. As a family, we were on holiday the other week and we met someone I knew “Well fancy seeing you here”, I said.

Should I have been surprised [see box 2] ?

Box 2: Assumption that all coincidences are equally likely.

In this situation I hadn’t said beforehand to my family that I would meet a particular person, at a specific event, on a certain day, at a point in time. It is an imprecise research question. As statisticians we can’t put numbers on coincidences like this, and maybe I shouldn’t have been at all surprised given the wide net that this question posed.

And now to the answer to my first question, i.e. Facebook birthdays. This is a more precise research question and it can be answered by statisticians. I am specifically talking about friends, (not work colleagues, doctors, dentists or whoever else I know), birthdays (not random events), and on a specific day (not any unforeseen day).

Usually in statistics we look at a table of critical values (e.g. z, t, and χ2, etc) to make a conclusion about our findings. In this case we use an online calculator. This tells me that I should be surprised if there were three people who shared the same birthday in less than 88 friends (this is my critical value).

And in true statistical fashion we use something called a test statistic to see how my observation in practice compares with the critical value. My test statistic is three people sharing the same birthday in 50 friends on Facebook. Since 50 is less than 88, I was correct in being surprised that three people share the same birthday in so few friends.

But then again, I did say earlier that we have to be aware of the assumptions !

And no comments please about my lack of friends.


Byron Jones and Robb Muirhead (2012) What a coincidence! It’s not as unlikely as you think Significance 9 (1) pp.40-42

Mario Cortina Borja (2013) The strong birthday problem Significance 10 (6) pp.18-20

In an earlier blog I discussed a presentation I gave to a group of school children about being a statistician (to one school in Edinburgh). You can find it here:

I found this interactive graphic, from the Office for National Statistics (ONS), which provides a picture of babies names in England & Wales – it’s not comparable with my presentation but it is an interesting way of showing the results (

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Here is an example of a presentation I recently gave entitled “Process Improvement & Design of Experiments – Lessons Learnt from a European Statistics Conference”:

Saturday, 11 January 2014

Primary school children learn about being a Statistician

It’s not every day that you get asked to explain what you do in your day-to-day job to someone outside your work. But I am always up for a challenge and because I like being a statistician I generally think it shouldn't be too difficult.

Well they were my long held thoughts until a local headmaster approached me to give a talk to a group of primary school children. The request came about because the school was due to hold a work focus week. As part of this exercise several parents were asked if they could provide presentations about the content of their work.

I tried to think about how I could describe my job in simple but easily understandable terms. I had previously read about the Up-Goer Five Text Editor, which challenges you to explain hard ideas using only the 'ten hundred' most common words, and I thought I would try and describe my job using only words from the list. This is what I came up with, and it allowed me to focus on what I should deliver in a presentation to the children:

I work with numbers and I have always worked with numbers. I write things on a computer that lets me get these numbers and allows me to handle them. I speak to people about them, and then I put them out using a paper which groups them all together.  My work can be hard to understand and some do not accept it without a get together before they are taken seriously. Sometimes people don't like the numbers and that causes some problems, they may be against what they say. Other times, maybe when the numbers go down, they are liked by everyone. In the end, I like to think that my work helps to give all people a better life.

So I started with a blank sheet of paper and for a while I was stumped, and then it occurred to me that I should give a talk about the names of children born in Scotland. In this way I could engage the children in a discussion about data collection, analysis and interpretation, and finally dissemination. Of course, I didn’t use those words exactly but they are the specialist skills that we need to develop as professional statisticians.

Armed with my presentation I headed to the school’s classroom. Forty children aged between 8 and 10 years old were in attendance, and they were accompanied by their teachers. There wasn’t much space available so some children sat on the floor, others in the room sat at their tables.

As an introduction I said to the children why I liked numbers and then I gave them some idea about the kind of numbers we can encounter in our everyday working lives. To ensure there was some interaction I asked them if they knew about numbers that included a decimal point, and others that started with £ and % - they were very forthcoming. I covered some of my other examples over and asked the group if they could think of any that remain. Someone enthusiastically put their hand up, and after my acknowledgement they replied “Yes, euros”.

Given it was work focus week it was of course appropriate that I went on to tell them about how I came into my career as a statistician and the training I had undertaken. Subsequently I then discussed my specific example of statistics i.e. the names of children born in Scotland. Here are two slides that I used to provide an example of these statistics. I didn't just want to give them a presentation and end up with 40 blank faces, so I continued with the interaction approach ….

A boy called Ethan put his hand up and said that his name was at the top – he knew several Ethan’s at schools in Edinburgh, then Sophie put her hand up. After hearing from quite a few children I then revealed the answer. Ethan was at number 5 and I gave them several reasons why it went against the thoughts of Ethan in the class e.g. Edinburgh may not reflect the national figures, and it is now at least 8 years after they were born and times change.

hadn't originally appreciated how much interest my statistics example would generate. I have only paraphrased a small part of the discussion. At the time this made me realise how passionate I am about statistics. It also let me flow into a final discussion about why we need to work and I gave several examples of this.

In summary, the presentation was received with so much enthusiasm and nearly every one of the children asked at least one question. I have transcribed the comments of one of the children who commented after the event:

“Thank you for coming in I liked all the new facts you told us about. I never knew that people made charts of names and other similar stuff. I enjoyed doing the wee sums you asked us. Your job looks exciting, I might want to do it when I'm older. I thought it was very interesting when you told us about the numbers you used and the charts. It looked complicated. I’d like a job a little like yours because I like doing maths. Thank you for coming in to talk to us and for giving up your time.”

Ian Morton has worked as a statistician for a number of years. In 2013, he entered his presentation into The Greenfield Challenge (a competition run by the European Network of Business and Industrial Statisticians (ENBIS)), and he won an award of book tokens for his contribution.

Note: The views expressed are his own and do not represent the views of any organisation he has worked for in the past or at present.